Your data matches 109 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001820
(load all 2 compositions to match this statistic)
Mapping
St001820: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 2 = 3 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 2 = 3 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2 = 3 - 1
Description
The size of the image of the pop stack sorting operator. The pop stack sorting operator is defined by $Pop_L^\downarrow(x) = x\wedge\bigwedge\{y\in L\mid y\lessdot x\}$. This statistic returns the size of $Pop_L^\downarrow(L)\}$.
Matching statistic: St001626
(load all 2 compositions to match this statistic)
Mapping
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001626: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(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)
 => 2
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 3
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 3
Description
The number of maximal proper sublattices of a lattice.
Matching statistic: St000528
Mapping
Mp00263: Lattices —join irreducibles⟶ Posets
St000528: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1)],2)
 => ([],1)
 => 1 = 2 - 1
([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 2 = 3 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 1 = 2 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3 = 4 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => 1 = 2 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => 2 = 3 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 5 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
Description
The height of a poset. This equals the rank of the poset [[St000080]] plus one.
Matching statistic: St000912
Mapping
Mp00263: Lattices —join irreducibles⟶ Posets
St000912: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1)],2)
 => ([],1)
 => 1 = 2 - 1
([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 2 = 3 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 1 = 2 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3 = 4 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => 1 = 2 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => 2 = 3 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 5 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
Description
The number of maximal antichains in a poset.
Matching statistic: St001343
Mapping
Mp00263: Lattices —join irreducibles⟶ Posets
St001343: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1)],2)
 => ([],1)
 => 1 = 2 - 1
([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 2 = 3 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 1 = 2 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3 = 4 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => 1 = 2 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => 2 = 3 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 5 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
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: St001717
Mapping
Mp00263: Lattices —join irreducibles⟶ Posets
St001717: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1)],2)
 => ([],1)
 => 1 = 2 - 1
([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 2 = 3 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 1 = 2 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3 = 4 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => 1 = 2 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => 2 = 3 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 5 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
Description
The largest size of an interval in a poset.
Matching statistic: St000080
Mapping
Mp00263: Lattices —join irreducibles⟶ Posets
St000080: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1)],2)
 => ([],1)
 => 0 = 2 - 2
([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 1 = 3 - 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 0 = 2 - 2
([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 2 = 4 - 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => 0 = 2 - 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => 1 = 3 - 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 5 - 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(1,2)],3)
 => 1 = 3 - 2
Description
The rank of the poset.
Matching statistic: St000469
(load all 4 compositions to match this statistic)
Mapping
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000469: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 2
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(2,4),(3,4)],5)
 => 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 3
Description
The distinguishing number of a graph. This is the minimal number of colours needed to colour the vertices of a graph, such that only the trivial automorphism of the graph preserves the colouring. For connected graphs, this statistic is at most one plus the maximal degree of the graph, with equality attained for complete graphs, complete bipartite graphs and the cycle with five vertices, see Theorem 4.2 of [2].
Matching statistic: St000776
Mapping
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000776: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 2
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(2,4),(3,4)],5)
 => 3
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 3
Description
The maximal multiplicity of an eigenvalue in a graph.
Matching statistic: St000986
(load all 3 compositions to match this statistic)
Mapping
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000986: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 2
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(2,4),(3,4)],5)
 => 3
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 3
Description
The multiplicity of the eigenvalue zero of the adjacency matrix of the graph.
The following 99 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001366The maximal multiplicity of a degree of a vertex of a graph. St001571The Cartan determinant of the integer partition. St001619The number of non-isomorphic sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St001691The number of kings in a graph. St001720The minimal length of a chain of small intervals in a lattice. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St000093The cardinality of a maximal independent set of vertices of a graph. St000147The largest part of an integer partition. St000482The (zero)-forcing 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. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St001286The annihilation number of a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001389The number of partitions of the same length below the given integer partition. St001616The number of neutral elements in a lattice. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001622The number of join-irreducible elements of a lattice. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000013The height of a Dyck path. St000160The multiplicity of the smallest part of a partition. St000443The number of long tunnels of a Dyck path. St000444The length of the maximal rise of a Dyck path. St000475The number of parts equal to 1 in a partition. St000674The number of hills of a Dyck path. St000982The length of the longest constant subword. St000992The alternating sum of the parts of an integer partition. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001297The number of indecomposable non-injective projective modules minus the number of indecomposable non-injective projective modules that have reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001498The normalised height of a Nakayama algebra with magnitude 1. St001656The monophonic position number of a graph. St001933The largest multiplicity of a part in an integer partition. St000010The length of the partition. St000024The number of double up and double down steps 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. St000442The maximal area to the right of an up step of a Dyck path. St000822The Hadwiger number of the graph. St000877The depth of the binary word interpreted as a path. St001029The size of the core of a graph. St001091The number of parts in an integer partition whose next smaller part has the same size. St001116The game chromatic number of a graph. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001330The hat guessing number of a graph. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001670The connected partition number of a graph. St001883The mutual visibility number of a graph. St001963The tree-depth of a graph. St000272The treewidth of a graph. St000362The size of a minimal vertex cover of a graph. St000536The pathwidth of a graph. St000931The number of occurrences of the pattern UUU in a Dyck path. St001176The size of a partition minus its first part. St001231The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. St001234The number of indecomposable three dimensional modules with projective dimension one. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001358The largest degree of a regular subgraph of a graph. St001644The dimension of a graph. St001812The biclique partition number of a graph. St001962The proper pathwidth of a graph. St001668The number of points of the poset minus the width of the poset. St000668The least common multiple of the parts of the partition. St000708The product of the parts of an integer partition. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St000454The largest eigenvalue of a graph if it is integral. St001651The Frankl number of a lattice. St000741The Colin de Verdière graph invariant. St000656The number of cuts of a poset. 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. St000327The number of cover relations in a poset. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St001637The number of (upper) dissectors of a poset. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St001875The number of simple modules with projective dimension at most 1. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. 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.