Your data matches 205 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000189
(load all 2 compositions to match this statistic)
Mapping
St000189: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([],2)
 => 2
([(0,1)],2)
 => 2
([],3)
 => 3
([(1,2)],3)
 => 3
([(0,1),(0,2)],3)
 => 3
([(0,2),(2,1)],3)
 => 3
([(0,2),(1,2)],3)
 => 3
Description
The number of elements in the poset.
Matching statistic: St001636
(load all 3 compositions to match this statistic)
Mapping
St001636: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([],2)
 => 2
([(0,1)],2)
 => 2
([],3)
 => 3
([(1,2)],3)
 => 3
([(0,1),(0,2)],3)
 => 3
([(0,2),(2,1)],3)
 => 3
([(0,2),(1,2)],3)
 => 3
Description
The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset.
Matching statistic: St000228
(load all 9 compositions to match this statistic)
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St000228: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [1]
 => 1
([],2)
 => [1,1]
 => 2
([(0,1)],2)
 => [2]
 => 2
([],3)
 => [1,1,1]
 => 3
([(1,2)],3)
 => [2,1]
 => 3
([(0,1),(0,2)],3)
 => [2,1]
 => 3
([(0,2),(2,1)],3)
 => [3]
 => 3
([(0,2),(1,2)],3)
 => [2,1]
 => 3
Description
The size of a partition. This statistic is the constant statistic of the level sets.
Matching statistic: St000459
(load all 14 compositions to match this statistic)
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St000459: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [1]
 => 1
([],2)
 => [1,1]
 => 2
([(0,1)],2)
 => [2]
 => 2
([],3)
 => [1,1,1]
 => 3
([(1,2)],3)
 => [2,1]
 => 3
([(0,1),(0,2)],3)
 => [2,1]
 => 3
([(0,2),(2,1)],3)
 => [3]
 => 3
([(0,2),(1,2)],3)
 => [2,1]
 => 3
Description
The hook length of the base cell of a partition. This is also known as the perimeter of a partition. In particular, the perimeter of the empty partition is zero.
Matching statistic: St000460
(load all 9 compositions to match this statistic)
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St000460: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [1]
 => 1
([],2)
 => [1,1]
 => 2
([(0,1)],2)
 => [2]
 => 2
([],3)
 => [1,1,1]
 => 3
([(1,2)],3)
 => [2,1]
 => 3
([(0,1),(0,2)],3)
 => [2,1]
 => 3
([(0,2),(2,1)],3)
 => [3]
 => 3
([(0,2),(1,2)],3)
 => [2,1]
 => 3
Description
The hook length of the last cell along the main diagonal of an integer partition.
Matching statistic: St000479
(load all 3 compositions to match this statistic)
Mapping
Mp00074: Posets —to graph⟶ Graphs
St000479: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => 1
([],2)
 => ([],2)
 => 2
([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],3)
 => 3
([(1,2)],3)
 => ([(1,2)],3)
 => 3
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 3
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
Description
The Ramsey number of a graph. This is the smallest integer $n$ such that every two-colouring of the edges of the complete graph $K_n$ contains a (not necessarily induced) monochromatic copy of the given graph. [1] Thus, the Ramsey number of the complete graph $K_n$ is the ordinary Ramsey number $R(n,n)$. Very few of these numbers are known, in particular, it is only known that $43\leq R(5,5)\leq 48$. [2,3,4,5]
Matching statistic: St000870
(load all 14 compositions to match this statistic)
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St000870: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [1]
 => 1
([],2)
 => [1,1]
 => 2
([(0,1)],2)
 => [2]
 => 2
([],3)
 => [1,1,1]
 => 3
([(1,2)],3)
 => [2,1]
 => 3
([(0,1),(0,2)],3)
 => [2,1]
 => 3
([(0,2),(2,1)],3)
 => [3]
 => 3
([(0,2),(1,2)],3)
 => [2,1]
 => 3
Description
The product of the hook lengths of the diagonal cells in an integer partition. For a cell in the Ferrers diagram of a partition, the hook length is given by the number of boxes to its right plus the number of boxes below + 1. This statistic is the product of the hook lengths of the diagonal cells $(i,i)$ of a partition.
Matching statistic: St001318
(load all 3 compositions to match this statistic)
Mapping
Mp00074: Posets —to graph⟶ Graphs
St001318: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => 1
([],2)
 => ([],2)
 => 2
([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],3)
 => 3
([(1,2)],3)
 => ([(1,2)],3)
 => 3
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 3
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
Description
The number of vertices of the largest induced subforest with the same number of connected components of a graph.
Matching statistic: St001321
(load all 3 compositions to match this statistic)
Mapping
Mp00074: Posets —to graph⟶ Graphs
St001321: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => 1
([],2)
 => ([],2)
 => 2
([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],3)
 => 3
([(1,2)],3)
 => ([(1,2)],3)
 => 3
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 3
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
Description
The number of vertices of the largest induced subforest of a graph.
Matching statistic: St001380
(load all 9 compositions to match this statistic)
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St001380: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [1]
 => 1
([],2)
 => [1,1]
 => 2
([(0,1)],2)
 => [2]
 => 2
([],3)
 => [1,1,1]
 => 3
([(1,2)],3)
 => [2,1]
 => 3
([(0,1),(0,2)],3)
 => [2,1]
 => 3
([(0,2),(2,1)],3)
 => [3]
 => 3
([(0,2),(1,2)],3)
 => [2,1]
 => 3
Description
The number of monomer-dimer tilings of a Ferrers diagram. For a hook of length $n$, this is the $n$-th Fibonacci number.
The following 195 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
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. St001672The restrained domination number of a graph. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St000171The degree of the graph. St000293The number of inversions of a binary word. St000519The largest length of a factor maximising the subword complexity. St000636The hull number of a graph. St000922The minimal number such that all substrings of this length are unique. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001034The area of the parallelogram polyomino associated with the Dyck path. St001342The number of vertices in the center of a graph. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001746The coalition number of a graph. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000921The number of internal inversions of a binary word. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001110The 3-dynamic chromatic number of a graph. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001437The flex of a binary word. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001725The harmonious chromatic number of a graph. St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000050The depth or height of a binary tree. St000144The pyramid weight of the Dyck path. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St000209Maximum difference of elements in cycles. St000210Minimum over maximum difference of elements in cycles. St000216The absolute length of a permutation. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000246The number of non-inversions of a permutation. St000288The number of ones in a binary word. St000290The major index of a binary word. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000336The leg major index of a standard tableau. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000383The last part of an integer composition. St000393The number of strictly increasing runs in a binary word. St000395The sum of the heights of the peaks of a Dyck path. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000458The number of permutations obtained by switching adjacencies or successions. St000494The number of inversions of distance at most 3 of a permutation. St000564The number of occurrences of the pattern {{1},{2}} in a set partition. St000657The smallest part of an integer composition. St000719The number of alignments in a perfect matching. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000744The length of the path to the largest entry in a standard Young tableau. St000808The number of up steps of the associated bargraph. St000809The reduced reflection length of the permutation. St000863The length of the first row of the shifted shape of a permutation. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000924The number of topologically connected components of a perfect matching. St000957The number of Bruhat lower covers of a permutation. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001120The length of a longest path in a graph. St001161The major index north count of a Dyck path. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001267The length of the Lyndon factorization of the binary word. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001480The number of simple summands of the module J^2/J^3. St001485The modular major index of a binary word. St001500The global dimension of magnitude 1 Nakayama algebras. St001523The degree of symmetry of a Dyck path. St001554The number of distinct nonempty subtrees of a binary tree. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001757The number of orbits of toric promotion on a graph. St001759The Rajchgot index of a permutation. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001958The degree of the polynomial interpolating the values of a permutation. St000026The position of the first return of a Dyck path. St000044The number of vertices of the unicellular map given by a perfect matching. St000058The order of a permutation. St000147The largest part of an integer partition. St000384The maximal part of the shifted composition of an integer partition. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000501The size of the first part in the decomposition of a permutation. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000668The least common multiple of the parts of the partition. St000673The number of non-fixed points of a permutation. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St000784The maximum of the length and the largest part of the integer partition. St000844The size of the largest block in the direct sum decomposition of a permutation. St000876The number of factors in the Catalan decomposition of a binary word. St000885The number of critical steps in the Catalan decomposition of a binary word. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001160The number of proper blocks (or intervals) of a permutations. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001245The cyclic maximal difference between two consecutive entries of a permutation. St001274The number of indecomposable injective modules with projective dimension equal to two. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse 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. St001345The Hamming dimension of a graph. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001707The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them. St001955The number of natural descents for set-valued two row standard Young tableaux. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000806The semiperimeter of the associated bargraph. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. 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. St001468The smallest fixpoint of a permutation. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000080The rank of the poset. St000528The height of a poset. St000906The length of the shortest maximal chain in a poset. St000643The size of the largest orbit of antichains under Panyushev complementation. St000941The number of characters of the symmetric group whose value on the partition is even. St000259The diameter of a connected graph. St000625The sum of the minimal distances to a greater element. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St001074The number of inversions of the cyclic embedding of a permutation. St001340The cardinality of a minimal non-edge isolating set of a graph. St000060The greater neighbor of the maximum. St000093The cardinality of a maximal independent set of vertices of a graph. St000273The domination number of a graph. St000327The number of cover relations in a poset. St000385The number of vertices with out-degree 1 in a binary tree. St000402Half the size of the symmetry class of a permutation. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000530The number of permutations with the same descent word as the given permutation. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000916The packing number of a graph. St001246The maximal difference between two consecutive entries of a permutation. St001286The annihilation number 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. St001637The number of (upper) dissectors of a poset. St001829The common independence number of a graph. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001388The number of non-attacking neighbors of a permutation. St001930The weak major index of a binary word. St001875The number of simple modules with projective dimension at most 1. St001668The number of points of the poset minus the width of the poset. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001623The number of doubly irreducible elements of a lattice. St001820The size of the image of the pop stack sorting operator. St001626The number of maximal proper sublattices of a lattice. St001720The minimal length of a chain of small intervals in a lattice. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001645The pebbling number of a connected graph. St000741The Colin de Verdière graph invariant. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000454The largest eigenvalue of a graph if it is integral. St000045The number of linear extensions of a binary tree. St000782The indicator function of whether a given perfect matching is an L & P matching. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St000219The number of occurrences of the pattern 231 in a permutation. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St000455The second largest eigenvalue of a graph if it is integral. St000264The girth of a graph, which is not a tree. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St001060The distinguishing index of a graph. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset.