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Your data matches 278 different statistics following compositions of up to 3 maps.
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Matching statistic: St000263
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
([],1)
=> 0
([],2)
=> 0
([(0,1)],2)
=> 1
([],3)
=> 0
([(1,2)],3)
=> 1
([(0,2),(1,2)],3)
=> 4
([(0,1),(0,2),(1,2)],3)
=> 3
Description
The Szeged index of a graph.
Matching statistic: St000265
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
([],1)
=> 0
([],2)
=> 0
([(0,1)],2)
=> 1
([],3)
=> 0
([(1,2)],3)
=> 1
([(0,2),(1,2)],3)
=> 4
([(0,1),(0,2),(1,2)],3)
=> 3
Description
The Wiener index of a graph.
This is the sum of the distances of all pairs of vertices.
Matching statistic: St000972
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],1)
=> 1 = 0 + 1
([],2)
=> 1 = 0 + 1
([(0,1)],2)
=> 2 = 1 + 1
([],3)
=> 1 = 0 + 1
([(1,2)],3)
=> 2 = 1 + 1
([(0,2),(1,2)],3)
=> 4 = 3 + 1
([(0,1),(0,2),(1,2)],3)
=> 5 = 4 + 1
Description
The composition number of a graph.
This is the number of set partitions of the vertex set of the graph, such that the subgraph induced by each block is connected.
Matching statistic: St001474
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],1)
=> 1 = 0 + 1
([],2)
=> 1 = 0 + 1
([(0,1)],2)
=> 2 = 1 + 1
([],3)
=> 1 = 0 + 1
([(1,2)],3)
=> 2 = 1 + 1
([(0,2),(1,2)],3)
=> 4 = 3 + 1
([(0,1),(0,2),(1,2)],3)
=> 5 = 4 + 1
Description
The evaluation of the Tutte polynomial of the graph at (x,y) equal to (2,-1).
Matching statistic: St000550
Values
([],1)
=> ([],1)
=> 1 = 0 + 1
([],2)
=> ([],1)
=> 1 = 0 + 1
([(0,1)],2)
=> ([(0,1)],2)
=> 2 = 1 + 1
([],3)
=> ([],1)
=> 1 = 0 + 1
([(1,2)],3)
=> ([(0,1)],2)
=> 2 = 1 + 1
([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 3 + 1
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 5 = 4 + 1
Description
The number of modular elements of a lattice.
A pair (x,y) of elements of a lattice L is a modular pair if for every z≥y we have that (y∨x)∧z=y∨(x∧z). An element x is left-modular if (x,y) is a modular pair for every y∈L, and is modular if both (x,y) and (y,x) are modular pairs for every y∈L.
Matching statistic: St000551
Values
([],1)
=> ([],1)
=> 1 = 0 + 1
([],2)
=> ([],1)
=> 1 = 0 + 1
([(0,1)],2)
=> ([(0,1)],2)
=> 2 = 1 + 1
([],3)
=> ([],1)
=> 1 = 0 + 1
([(1,2)],3)
=> ([(0,1)],2)
=> 2 = 1 + 1
([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 3 + 1
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 5 = 4 + 1
Description
The number of left modular elements of a lattice.
A pair (x,y) of elements of a lattice L is a modular pair if for every z≥y we have that (y∨x)∧z=y∨(x∧z). An element x is left-modular if (x,y) is a modular pair for every y∈L.
Matching statistic: St001592
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
([],2)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 2 = 1 + 1
([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
([(1,2)],3)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 3 + 1
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 5 = 4 + 1
Description
The maximal number of simple paths between any two different vertices of a graph.
Matching statistic: St001706
Values
([],1)
=> ([],0)
=> 1 = 0 + 1
([],2)
=> ([],0)
=> 1 = 0 + 1
([(0,1)],2)
=> ([],1)
=> 2 = 1 + 1
([],3)
=> ([],0)
=> 1 = 0 + 1
([(1,2)],3)
=> ([],1)
=> 2 = 1 + 1
([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 4 = 3 + 1
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 5 = 4 + 1
Description
The number of closed sets in a graph.
A subset S of the set of vertices is a closed set, if for any pair of distinct elements of S the intersection of the corresponding neighbourhoods is a subset of S:
∀a,b∈S:N(a)∩N(b)⊆S.
Matching statistic: St001619
Values
([],1)
=> ([],1)
=> 2 = 0 + 2
([],2)
=> ([],1)
=> 2 = 0 + 2
([(0,1)],2)
=> ([(0,1)],2)
=> 3 = 1 + 2
([],3)
=> ([],1)
=> 2 = 0 + 2
([(1,2)],3)
=> ([(0,1)],2)
=> 3 = 1 + 2
([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 5 = 3 + 2
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 6 = 4 + 2
Description
The number of non-isomorphic sublattices of a lattice.
Matching statistic: St001666
Values
([],1)
=> ([],1)
=> 2 = 0 + 2
([],2)
=> ([],1)
=> 2 = 0 + 2
([(0,1)],2)
=> ([(0,1)],2)
=> 3 = 1 + 2
([],3)
=> ([],1)
=> 2 = 0 + 2
([(1,2)],3)
=> ([(0,1)],2)
=> 3 = 1 + 2
([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 5 = 3 + 2
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 6 = 4 + 2
Description
The number of non-isomorphic subposets of a lattice which are lattices.
The following 268 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000009The charge of a standard tableau. St000059The inversion number of a standard tableau as defined by Haglund and Stevens. St001127The sum of the squares of the parts of a partition. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001764The number of non-convex subsets of vertices in a graph. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St000189The number of elements in the poset. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001717The largest size of an interval in a poset. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000169The cocharge of a standard tableau. St000330The (standard) major index of a standard tableau. St001697The shifted natural comajor index of a standard Young tableau. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000300The number of independent sets of vertices of a graph. St000420The number of Dyck paths that are weakly above a Dyck path. St000421The number of Dyck paths that are weakly below a Dyck path, except for the path itself. St000418The number of Dyck paths that are weakly below a Dyck path. St001645The pebbling number of a connected graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000302The determinant of the distance matrix of a connected graph. St000309The number of vertices with even degree. St000466The Gutman (or modified Schultz) index of a connected graph. St001117The game chromatic index of a graph. St001249Sum of the odd parts of a partition. St001341The number of edges in the center of a graph. St001477The number of nowhere zero 5-flows of a graph. St001478The number of nowhere zero 4-flows of a graph. St001541The Gini index of an integer partition. St001561The value of the elementary symmetric function evaluated at 1. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001783The number of odd automorphisms of a graph. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001827The number of two-component spanning forests of a graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000005The bounce statistic of a Dyck path. St000006The dinv of a Dyck path. St000008The major index of the composition. St000012The area of a Dyck path. St000016The number of attacking pairs of a standard tableau. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000081The number of edges of a graph. St000088The row sums of the character table of the symmetric group. St000379The number of Hamiltonian cycles in a graph. St000509The diagonal index (content) of a partition. St000567The sum of the products of all pairs of parts. St000683The number of points below the Dyck path such that the diagonal to the north-east hits the path between two down steps, and the diagonal to the north-west hits the path between two up steps. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. 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. St000867The sum of the hook lengths in the first row of an integer partition. St000946The sum of the skew hook positions in a Dyck path. St000951The dimension of Ext1(D(A),A) of the corresponding LNakayama algebra. St000976The sum of the positions of double up-steps of a Dyck path. St000984The number of boxes below precisely one peak. St000992The alternating sum of the parts of an integer partition. St001055The Grundy value for the game of removing cells of a row in 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. St001161The major index north count of a Dyck path. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. St001243The sum of coefficients in the Schur basis of certain LLT polynomials associated with a Dyck path. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001262The dimension of the maximal parabolic seaweed algebra corresponding to the partition. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001347The number of pairs of vertices of a graph having the same neighbourhood. St001602The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on endofunctions. St001610The number of coloured endofunctions such that the multiplicities of colours are given by a partition. St001649The length of a longest trail in a graph. St001651The Frankl number of a lattice. St001688The sum of the squares of the heights of the peaks of a Dyck path. St001809The index of the step at the first peak of maximal height in a Dyck path. St001845The number of join irreducibles minus the rank of a lattice. St001931The weak major index of an integer composition regarded as a word. St001932The number of pairs of singleton blocks in the noncrossing set partition corresponding to a Dyck path, that can be merged to create another noncrossing set partition. St001961The sum of the greatest common divisors of all pairs of parts. St000454The largest eigenvalue of a graph if it is integral. St000741The Colin de Verdière graph invariant. St000422The energy of a graph, if it is integral. St000014The number of parking functions supported by a Dyck path. St000026The position of the first return of a Dyck path. St000117The number of centered tunnels of a Dyck path. St000296The length of the symmetric border of a binary word. St000348The non-inversion sum of a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000543The size of the conjugacy class of a binary word. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000869The sum of the hook lengths of an integer partition. St000874The position of the last double rise in a Dyck path. St000947The major index east count of a Dyck path. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001126Number of simple module that are 1-regular 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. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001227The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001254The vector space dimension of the first extension-group between A/soc(A) and J when A is the corresponding Nakayama algebra with Jacobson radical J. St001278The number of indecomposable modules that are fixed by τΩ1 composed with its inverse in the corresponding Nakayama algebra. St001289The vector space dimension of the n-fold tensor product of D(A), where n is maximal such that this n-fold tensor product is nonzero. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001371The length of the longest Yamanouchi prefix of a binary word. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001480The number of simple summands of the module J^2/J^3. St001498The normalised height of a Nakayama algebra with magnitude 1. St001500The global dimension of magnitude 1 Nakayama algebras. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001808The box weight or horizontal decoration of a Dyck path. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001872The number of indecomposable injective modules with even projective dimension in the corresponding Nakayama algebra. St001885The number of binary words with the same proper border set. St001910The height of the middle non-run of a Dyck path. St001930The weak major index of a binary word. St001956The comajor index for set-valued two-row standard Young tableaux. St001959The product of the heights of the peaks of a Dyck path. St000456The monochromatic index of a connected graph. St000137The Grundy value of an integer partition. St000455The second largest eigenvalue of a graph if it is integral. St000467The hyper-Wiener index of a connected graph. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St001118The acyclic chromatic index of a graph. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001176The size of a partition minus its first part. St001383The BG-rank of an integer partition. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001525The number of symmetric hooks on the diagonal of a partition. St001529The number of monomials in the expansion of the nabla operator applied to the power-sum symmetric function indexed by the partition. St001562The value of the complete homogeneous symmetric function evaluated at 1. St001563The value of the power-sum symmetric function evaluated at 1. St001564The value of the forgotten symmetric functions when all variables set to 1. St001593This is the number of standard Young tableaux of the given shifted shape. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001939The number of parts that are equal to their multiplicity in the integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001330The hat guessing number of a graph. St001626The number of maximal proper sublattices of a lattice. St000010The length of the partition. St000142The number of even parts of a partition. St000143The largest repeated part of a partition. St000145The Dyson rank of a partition. St000147The largest part of an integer partition. St000148The number of odd parts of a partition. St000149The number of cells of the partition whose leg is zero and arm is odd. St000150The floored half-sum of the multiplicities of a partition. St000159The number of distinct parts of the integer partition. St000160The multiplicity of the smallest part of a partition. St000183The side length of the Durfee square of an integer partition. St000185The weighted size of a partition. St000212The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. St000228The size of a partition. St000256The number of parts from which one can substract 2 and still get an integer partition. St000257The number of distinct parts of a partition that occur at least twice. St000289The decimal representation of a binary word. St000295The length of the border of a binary word. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000340The number of non-final maximal constant sub-paths of length greater than one. St000347The inversion sum of a binary word. St000369The dinv deficit of a Dyck path. St000376The bounce deficit of a Dyck path. St000377The dinv defect of an integer partition. St000378The diagonal inversion number of an integer partition. St000384The maximal part of the shifted composition of an integer partition. St000389The number of runs of ones of odd length in a binary word. St000391The sum of the positions of the ones in a binary word. St000442The maximal area to the right of an up step of a Dyck path. St000459The hook length of the base cell of a partition. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000475The number of parts equal to 1 in a partition. St000480The number of lower covers of a partition in dominance order. St000481The number of upper covers of a partition in dominance order. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000519The largest length of a factor maximising the subword complexity. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000547The number of even non-empty partial sums of an integer partition. St000548The number of different non-empty partial sums of an integer partition. St000549The number of odd partial sums of an integer partition. St000644The number of graphs with given frequency partition. St000658The number of rises of length 2 of a Dyck path. St000659The number of rises of length at least 2 of a Dyck path. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000705The number of semistandard tableaux on a given integer partition of n with maximal entry n. St000712The number of semistandard Young tableau of given shape, with entries at most 4. St000715The number of semistandard Young tableaux of given shape and entries at most 3. St000762The sum of the positions of the weak records of an integer composition. St000783The side length of the largest staircase partition fitting into a partition. St000784The maximum of the length and the largest part of the integer partition. St000792The Grundy value for the game of ruler on a binary word. St000810The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to monomial symmetric functions. St000811The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to Schur symmetric functions. St000812The sum of the entries in the column specified by the partition of the change of basis matrix from complete homogeneous symmetric functions to monomial symmetric functions. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000878The number of ones minus the number of zeros of a binary word. St000885The number of critical steps in the Catalan decomposition of a binary word. St000897The number of different multiplicities of parts of an integer partition. St000921The number of internal inversions of a binary word. St000954Number of times the corresponding LNakayama algebra has Exti(D(A),A)=0 for i>0. St000964Gives the dimension of Ext^g(D(A),A) of the corresponding LNakayama algebra, when g denotes the global dimension of that algebra. St000965The sum of the dimension of Ext^i(D(A),A) for i=1,. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001010Number of indecomposable injective modules with projective dimension g-1 when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001026The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St001091The number of parts in an integer partition whose next smaller part has the same size. St001092The number of distinct even parts of a partition. St001121The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition. St001129The product of the squares of the parts of a partition. St001139The number of occurrences of hills of size 2 in a Dyck path. St001164Number of indecomposable injective modules whose socle has projective dimension at most g-1 (g the global dimension) minus the number of indecomposable projective-injective modules. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001194The injective dimension of A/AfA in the corresponding Nakayama algebra A when Af is the minimal faithful projective-injective left A-module St001228The vector space dimension of the space of module homomorphisms between J and itself when J denotes the Jacobson radical of the corresponding Nakayama algebra. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001242The toal dimension of certain Sn modules determined by LLT polynomials associated with a Dyck path. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001252Half the sum of the even parts of a partition. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001280The number of parts of an integer partition that are at least two. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001413Half the length of the longest even length palindromic prefix of a binary word. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001424The number of distinct squares in a binary word. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001484The number of singletons of an integer partition. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001524The degree of symmetry of a binary word. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001587Half of the largest even part of an integer partition. St001657The number of twos in an integer partition. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between eiJ and ejJ (the radical of the indecomposable projective modules). St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St001916The number of transient elements in the orbit of Bulgarian solitaire corresponding to a necklace. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001955The number of natural descents for set-valued two row standard Young tableaux.
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