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Your data matches 317 different statistics following compositions of up to 3 maps.
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Matching statistic: St001615
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
([],1)
=> 0 = 1 - 1
([(0,1)],2)
=> 1 = 2 - 1
([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
Description
The number of join prime elements of a lattice.
An element $x$ of a lattice $L$ is join-prime (or coprime) if $x \leq a \vee b$ implies $x \leq a$ or $x \leq b$ for every $a, b \in L$.
Matching statistic: St001617
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Values
([],1)
=> 0 = 1 - 1
([(0,1)],2)
=> 1 = 2 - 1
([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
Description
The dimension of the space of valuations of a lattice.
A valuation, or modular function, on a lattice $L$ is a function $v:L\mapsto\mathbb R$ satisfying
$$
v(a\vee b) + v(a\wedge b) = v(a) + v(b).
$$
It was shown by Birkhoff [1, thm. X.2], that a lattice with a positive valuation must be modular. This was sharpened by Fleischer and Traynor [2, thm. 1], which states that the modular functions on an arbitrary lattice are in bijection with the modular functions on its modular quotient [[Mp00196]].
Moreover, Birkhoff [1, thm. X.2] showed that the dimension of the space of modular functions equals the number of subsets of projective prime intervals.
Matching statistic: St001622
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(load all 4 compositions to match this statistic)
Values
([],1)
=> 0 = 1 - 1
([(0,1)],2)
=> 1 = 2 - 1
([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
Description
The number of join-irreducible elements of a lattice.
An element $j$ of a lattice $L$ is '''join irreducible''' if it is not the least element and if $j=x\vee y$, then $j\in\{x,y\}$ for all $x,y\in L$.
Matching statistic: St000528
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
Description
The height of a poset.
This equals the rank of the poset [[St000080]] plus one.
Matching statistic: St000912
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
Description
The number of maximal antichains in a poset.
Matching statistic: St001343
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(load all 3 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
Description
The dimension of the reduced incidence algebra of a poset.
The reduced incidence algebra of a poset is the subalgebra of the incidence algebra consisting of the elements which assign the same value to any two intervals that are isomorphic to each other as posets.
Thus, this statistic returns the number of non-isomorphic intervals of the poset.
Matching statistic: St001636
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
Description
The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset.
Matching statistic: St000080
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> 0 = 1 - 1
([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 2 - 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
Description
The rank of the poset.
Matching statistic: St001613
Values
([],1)
=> ([],1)
=> 0 = 1 - 1
([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 2 - 1
([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,3),(2,1),(3,2)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 3 = 4 - 1
Description
The binary logarithm of the size of the center of a lattice.
An element of a lattice is central if it is neutral and has a complement. The subposet induced by central elements is a Boolean lattice.
Matching statistic: St001782
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> 2 = 1 + 1
([(0,1)],2)
=> ([(0,1)],2)
=> 3 = 2 + 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 4 = 3 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 3 + 1
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 5 = 4 + 1
Description
The order of rowmotion on the set of order ideals of a poset.
The following 307 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000093The cardinality of a maximal independent set of vertices of a graph. St000147The largest part of an integer partition. St000184The size of the centralizer of any permutation of given cycle type. St000258The burning number of a graph. St000273The domination number of a graph. St000287The number of connected components of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000384The maximal part of the shifted composition of an integer partition. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000482The (zero)-forcing number of a graph. St000544The cop number of a graph. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000553The number of blocks of a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000784The maximum of the length and the largest part of the integer partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000916The packing number of a graph. St001093The detour number of a graph. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001286The annihilation number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001363The Euler characteristic of a graph according to Knill. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001389The number of partitions of the same length below the given integer partition. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001463The number of distinct columns in the nullspace of a graph. St001616The number of neutral elements in a lattice. St001720The minimal length of a chain of small intervals in a lattice. St001725The harmonious chromatic number of a graph. St001820The size of the image of the pop stack sorting operator. St001828The Euler characteristic of a graph. St001829The common independence number of a graph. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000069The number of maximal elements of a poset. St000259The diameter of a connected graph. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000474Dyson's crank of a partition. St000668The least common multiple of the parts of the partition. St000778The metric dimension of a graph. St001117The game chromatic index of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001345The Hamming dimension of a graph. St001512The minimum rank of a graph. St001571The Cartan determinant of the integer partition. St001619The number of non-isomorphic sublattices of a lattice. St001623The number of doubly irreducible elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St001949The rigidity index of a graph. St000010The length of the partition. St000011The number of touch points (or returns) of a Dyck path. St000015The number of peaks of a Dyck path. St000026The position of the first return of a Dyck path. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000172The Grundy number of a graph. St000189The number of elements in the poset. St000286The number of connected components of the complement of a graph. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000383The last part of an integer composition. St000459The hook length of the base cell of a partition. St000507The number of ascents of a standard tableau. St000519The largest length of a factor maximising the subword complexity. St000537The cutwidth of a graph. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000676The number of odd rises of a Dyck path. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000722The number of different neighbourhoods in a graph. St000734The last entry in the first row of a standard tableau. St000808The number of up steps of the associated bargraph. St000822The Hadwiger number of the graph. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000907The number of maximal antichains of minimal length in a poset. St000911The number of maximal antichains of maximal size in a poset. St000918The 2-limited packing number of a graph. St000922The minimal number such that all substrings of this length are unique. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001029The size of the core of a graph. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001116The game chromatic number of a graph. St001119The length of a shortest maximal path in a graph. St001202Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows:
St001250The number of parts of a partition that are not congruent 0 modulo 3. St001281The normalized isoperimetric number of a graph. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001315The dissociation number of a graph. St001316The domatic number of a graph. St001391The disjunction number of a graph. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001462The number of factors of a standard tableaux under concatenation. St001494The Alon-Tarsi number of a graph. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001530The depth of a Dyck path. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001670The connected partition number of a graph. St001675The number of parts equal to the part in the reversed composition. St001717The largest size of an interval in a poset. St001733The number of weak left to right maxima of a Dyck path. St001883The mutual visibility number of a graph. St001963The tree-depth of a graph. St000053The number of valleys of the Dyck path. St000070The number of antichains in a poset. St000104The number of facets in the order polytope of this poset. St000151The number of facets in the chain polytope of the poset. St000171The degree of the graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000272The treewidth of a graph. St000306The bounce count of a Dyck path. St000310The minimal degree of a vertex of a graph. St000331The number of upper interactions of a Dyck path. St000362The size of a minimal vertex cover of a graph. St000377The dinv defect of an integer partition. St000393The number of strictly increasing runs in a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000536The pathwidth of a graph. St000741The Colin de Verdière graph invariant. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. St000969We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001166Number of indecomposable projective non-injective modules with dominant dimension equal to the global dimension plus the number of indecomposable projective injective modules in the corresponding Nakayama algebra. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001170Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra. St001176The size of a partition minus its first part. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001205The number of non-simple indecomposable projective-injective modules of the algebra $eAe$ in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001223Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001323The independence gap of a graph. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001357The maximal degree of a regular spanning subgraph of a graph. St001358The largest degree of a regular subgraph of a graph. St001437The flex of a binary word. St001480The number of simple summands of the module J^2/J^3. St001492The number of simple modules that do not appear in the socle of the regular module or have no nontrivial selfextensions with the regular module in the corresponding Nakayama algebra. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001644The dimension of a graph. St001664The number of non-isomorphic subposets of a poset. St001674The number of vertices of the largest induced star graph in the graph. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001812The biclique partition number of a graph. St001962The proper pathwidth of a graph. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St000680The Grundy value for Hackendot on posets. St000717The number of ordinal summands of a poset. St000906The length of the shortest maximal chain in a poset. St000643The size of the largest orbit of antichains under Panyushev complementation. St001621The number of atoms of a lattice. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St000063The number of linear extensions of a certain poset defined for an integer partition. St000108The number of partitions contained in the given partition. St000180The number of chains of a poset. St000532The total number of rook placements on a Ferrers board. St000708The product of the parts of an integer partition. St001400The total number of Littlewood-Richardson tableaux of given shape. St000068The number of minimal elements in a poset. St000087The number of induced subgraphs. St000181The number of connected components of the Hasse diagram for the poset. St000228The size of a partition. St000460The hook length of the last cell along the main diagonal of an integer partition. St000469The distinguishing number of a graph. St000479The Ramsey number of a graph. St000527The width of the poset. St000531The leading coefficient of the rook polynomial of an integer partition. St000636The hull number of a graph. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St000908The length of the shortest maximal antichain in a poset. St000909The number of maximal chains of maximal size in a poset. St000917The open packing number of a graph. St000926The clique-coclique number of a graph. St001118The acyclic chromatic index of a graph. St001268The size of the largest ordinal summand in the poset. St001342The number of vertices in the center of a graph. St001360The number of covering relations in Young's lattice below a partition. St001366The maximal multiplicity of a degree of a vertex of a graph. St001368The number of vertices of maximal degree in a graph. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001399The distinguishing number of a poset. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001612The number of coloured multisets of cycles such that the multiplicities of colours are given by a partition. St001635The trace of the square of the Coxeter matrix of the incidence algebra of a poset. St001654The monophonic hull number of a graph. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001672The restrained domination number of a graph. St001746The coalition number of a graph. St001757The number of orbits of toric promotion on a graph. St001779The order of promotion on the set of linear extensions of a poset. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St000632The jump number of the poset. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001651The Frankl number of a lattice. St001827The number of two-component spanning forests of a graph. St001625The Möbius invariant of a lattice. St000327The number of cover relations in a poset. St000656The number of cuts of a poset. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001330The hat guessing number of a graph. St001642The Prague dimension of a graph. St001645The pebbling number of a connected graph. St000260The radius of a connected graph. St000274The number of perfect matchings of a graph. St000387The matching number of a graph. St000454The largest eigenvalue of a graph if it is integral. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000681The Grundy value of Chomp on Ferrers diagrams. St000744The length of the path to the largest entry in a standard Young tableau. St000932The number of occurrences of the pattern UDU in a Dyck path. St000937The number of positive values of the symmetric group character corresponding to the partition. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001271The competition number of a graph. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001570The minimal number of edges to add to make a graph Hamiltonian. St001792The arboricity of a graph. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000938The number of zeros of the symmetric group character corresponding to the partition. St001875The number of simple modules with projective dimension at most 1. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St000100The number of linear extensions of a poset. St000633The size of the automorphism group of a poset. St000910The number of maximal chains of minimal length in a poset. St000914The sum of the values of the Möbius function of a poset. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St000850The number of 1/2-balanced pairs in a poset. St001095The number of non-isomorphic posets with precisely one further covering relation. St000639The number of relations in a poset. St000640The rank of the largest boolean interval in a poset. St000641The number of non-empty boolean intervals in a poset. St001060The distinguishing index of a graph. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000706The product of the factorials of the multiplicities of an integer partition. St000993The multiplicity of the largest part of an integer partition. St001568The smallest positive integer that does not appear twice in the partition. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St000455The second largest eigenvalue of a graph if it is integral. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000567The sum of the products of all pairs of parts. St000929The constant term of the character polynomial of an integer partition. St001099The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled binary trees. St001100The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled trees. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001592The maximal number of simple paths between any two different vertices of a graph. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000456The monochromatic index of a connected graph. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St000379The number of Hamiltonian cycles in a graph. St000707The product of the factorials of the parts. St000770The major index of an integer partition when read from bottom to top. St000815The number of semistandard Young tableaux of partition weight of given shape. St000933The number of multipartitions of sizes given by an integer partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000478Another weight of a partition according to Alladi. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000934The 2-degree of an integer partition. St000941The number of characters of the symmetric group whose value on the partition is even. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons.
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