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Your data matches 66 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St001720
(load all 2 compositions to match this statistic)

Mapping

St001720: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => 3 = 1 + 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(0,3),(2,1),(3,2)],4)
 => 4 = 2 + 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 2 = 0 + 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 3 = 1 + 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 3 + 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 3 = 1 + 2

Description

The minimal length of a chain of small intervals in a lattice. An interval

$[a, b]$ is small if

$b$ is a join of elements covering

$a$ .

Matching statistic: St000717
(load all 3 compositions to match this statistic)

Mapping

Mp00263: Lattices —join irreducibles⟶ Posets
St000717: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 2 = 1 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 1 = 0 + 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => 1 = 0 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(1,2)],3)
 => 1 = 0 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => 2 = 1 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 1 + 1

Description

The number of ordinal summands of a poset. The ordinal sum of two posets

$P$ and

$Q$ is the poset having elements

$(p,0)$ and

$(q,1)$ for

$p\in P$ and

$q\in Q$ , and relations

$(a,0) < (b,0)$ if

$a < b$ in

$P$ ,

$(a,1) < (b,1)$ if

$a < b$ in

$Q$ , and

$(a,0) < (b,1)$ . This statistic is the length of the longest ordinal decomposition of a poset.

Matching statistic: St000906
(load all 3 compositions to match this statistic)

Mapping

Mp00263: Lattices —join irreducibles⟶ Posets
St000906: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 2 = 1 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 1 = 0 + 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => 1 = 0 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(1,2)],3)
 => 1 = 0 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => 2 = 1 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 1 + 1

Description

The length of the shortest maximal chain in a poset.

Matching statistic: St001820

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001820: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 1 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1 = 0 + 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 2 + 1
([(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)
 => 1 = 0 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1 = 0 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 2 = 1 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 3 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2 = 1 + 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: St000907
(load all 2 compositions to match this statistic)

Mapping

Mp00193: Lattices —to poset⟶ Posets
St000907: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3 = 1 + 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 2 + 2
([(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 = 0 + 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 2 = 0 + 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 3 = 1 + 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 3 + 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 3 = 1 + 2

Description

The number of maximal antichains of minimal length in a poset.

Matching statistic: St000080

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00263: Lattices —join irreducibles⟶ Posets
St000080: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 0
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 2
([(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
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 0
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(1,2)],3)
 => 1

Description

The rank of the poset.

Matching statistic: St000552
(load all 3 compositions to match this statistic)

Mapping

Mp00193: Lattices —to poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000552: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(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)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 0
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 0
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1

Description

The number of cut vertices of a graph. A cut vertex is one whose deletion increases the number of connected components.

Matching statistic: St001668
(load all 2 compositions to match this statistic)

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00263: Lattices —join irreducibles⟶ Posets
St001668: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 0
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 2
([(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
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 0
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(1,2)],3)
 => 1

Description

The number of points of the poset minus the width of the poset.

Matching statistic: St000273

Mapping

Mp00263: Lattices —join irreducibles⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000273: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => ([],2)
 => 2 = 1 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => ([(0,1)],2)
 => 1 = 0 + 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 0 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1 = 0 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => 2 = 1 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 2 = 1 + 1

Description

The domination number of a graph. The domination number of a graph is given by the minimum size of a dominating set of vertices. A dominating set of vertices is a subset of the vertex set of such that every vertex is either in this subset or adjacent to an element of this subset.

Matching statistic: St000287

Mapping

Mp00263: Lattices —join irreducibles⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000287: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => ([],2)
 => 2 = 1 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => ([(0,1)],2)
 => 1 = 0 + 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 0 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1 = 0 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => 2 = 1 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 2 = 1 + 1

Description

The number of connected components of a graph.

The following 56 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St000528The height of a poset. St000544The cop number of a graph. St000553The number of blocks of a graph. St000912The number of maximal antichains in a poset. St000916The packing number of a graph. St001322The size of a minimal independent dominating set in a graph. St001339The irredundance number of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001363The Euler characteristic of a graph according to Knill. St001717The largest size of an interval in a poset. St001829The common independence number of a graph. St000315The number of isolated vertices of a graph. St000643The size of the largest orbit of antichains under Panyushev complementation. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St000286The number of connected components of the complement of a graph. St001091The number of parts in an integer partition whose next smaller part has the same size. St001316The domatic number of a graph. St000160The multiplicity of the smallest part of a partition. St000312The number of leaves in a graph. St000475The number of parts equal to 1 in a partition. St000636The hull number of a graph. St000776The maximal multiplicity of an eigenvalue in a graph. St001060The distinguishing index of a graph. St001342The number of vertices in the center of a graph. St001368The number of vertices of maximal degree in a graph. St001479The number of bridges of a graph. St001571The Cartan determinant of the integer partition. St001654The monophonic hull number of a graph. St001691The number of kings in a graph. St001826The maximal number of leaves on a vertex of a graph. St001933The largest multiplicity of a part in an integer partition. St001672The restrained domination number of a graph. St000454The largest eigenvalue of a graph if it is integral. St001631The number of simple modules

$S$ with

$dim Ext^1(S,A)=1$ in the incidence algebra

$A$ of the poset. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000699The toughness times the least common multiple of 1,. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000941The number of characters of the symmetric group whose value on the partition is even. St001651The Frankl number of a lattice. St000327The number of cover relations in a poset. St001637The number of (upper) dissectors of a poset. St000656The number of cuts of a poset. St000680The Grundy value for Hackendot on posets. St000642The size of the smallest orbit of antichains under Panyushev complementation. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St000741The Colin de Verdière graph invariant. St000718The largest Laplacian eigenvalue of a graph if it is integral. St001875The number of simple modules with projective dimension at most 1. 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. St001330The hat guessing number of a graph. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.