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Your data matches 144 different statistics following compositions of up to 3 maps.
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Matching statistic: St000172
(load all 11 compositions to match this statistic)
(load all 11 compositions to match this statistic)
Values
([],1)
=> 1 = 2 - 1
([],2)
=> 1 = 2 - 1
([(0,1)],2)
=> 2 = 3 - 1
([],3)
=> 1 = 2 - 1
([(1,2)],3)
=> 2 = 3 - 1
([(0,2),(1,2)],3)
=> 2 = 3 - 1
([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([],4)
=> 1 = 2 - 1
([(2,3)],4)
=> 2 = 3 - 1
([(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,3),(1,2)],4)
=> 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
=> 3 = 4 - 1
([(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
Description
The Grundy number of a graph.
The Grundy number $\Gamma(G)$ is defined to be the largest $k$ such that $G$ admits a greedy $k$-coloring. Any order of the vertices of $G$ induces a greedy coloring by assigning to the $i$-th vertex in this order the smallest positive integer such that the partial coloring remains a proper coloring.
In particular, we have that $\chi(G) \leq \Gamma(G) \leq \Delta(G) + 1$, where $\chi(G)$ is the chromatic number of $G$ ([[St000098]]), and where $\Delta(G)$ is the maximal degree of a vertex of $G$ ([[St000171]]).
Matching statistic: St000822
(load all 7 compositions to match this statistic)
(load all 7 compositions to match this statistic)
Values
([],1)
=> 1 = 2 - 1
([],2)
=> 1 = 2 - 1
([(0,1)],2)
=> 2 = 3 - 1
([],3)
=> 1 = 2 - 1
([(1,2)],3)
=> 2 = 3 - 1
([(0,2),(1,2)],3)
=> 2 = 3 - 1
([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([],4)
=> 1 = 2 - 1
([(2,3)],4)
=> 2 = 3 - 1
([(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,3),(1,2)],4)
=> 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
=> 2 = 3 - 1
([(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> 3 = 4 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
Description
The Hadwiger number of the graph.
Also known as clique contraction number, this is the size of the largest complete minor.
Matching statistic: St001580
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
Values
([],1)
=> 1 = 2 - 1
([],2)
=> 1 = 2 - 1
([(0,1)],2)
=> 2 = 3 - 1
([],3)
=> 1 = 2 - 1
([(1,2)],3)
=> 2 = 3 - 1
([(0,2),(1,2)],3)
=> 2 = 3 - 1
([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([],4)
=> 1 = 2 - 1
([(2,3)],4)
=> 2 = 3 - 1
([(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,3),(1,2)],4)
=> 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
=> 2 = 3 - 1
([(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> 3 = 4 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
Description
The acyclic chromatic number of a graph.
This is the smallest size of a vertex partition $\{V_1,\dots,V_k\}$ such that each $V_i$ is an independent set and for all $i,j$ the subgraph inducted by $V_i\cup V_j$ does not contain a cycle.
Matching statistic: St001581
(load all 11 compositions to match this statistic)
(load all 11 compositions to match this statistic)
Values
([],1)
=> 1 = 2 - 1
([],2)
=> 1 = 2 - 1
([(0,1)],2)
=> 2 = 3 - 1
([],3)
=> 1 = 2 - 1
([(1,2)],3)
=> 2 = 3 - 1
([(0,2),(1,2)],3)
=> 2 = 3 - 1
([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([],4)
=> 1 = 2 - 1
([(2,3)],4)
=> 2 = 3 - 1
([(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,3),(1,2)],4)
=> 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
=> 3 = 4 - 1
([(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
Description
The achromatic number of a graph.
This is the maximal number of colours of a proper colouring, such that for any pair of colours there are two adjacent vertices with these colours.
Matching statistic: St000272
(load all 7 compositions to match this statistic)
(load all 7 compositions to match this statistic)
Values
([],1)
=> 0 = 2 - 2
([],2)
=> 0 = 2 - 2
([(0,1)],2)
=> 1 = 3 - 2
([],3)
=> 0 = 2 - 2
([(1,2)],3)
=> 1 = 3 - 2
([(0,2),(1,2)],3)
=> 1 = 3 - 2
([(0,1),(0,2),(1,2)],3)
=> 2 = 4 - 2
([],4)
=> 0 = 2 - 2
([(2,3)],4)
=> 1 = 3 - 2
([(1,3),(2,3)],4)
=> 1 = 3 - 2
([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(0,3),(1,2)],4)
=> 1 = 3 - 2
([(0,3),(1,2),(2,3)],4)
=> 1 = 3 - 2
([(1,2),(1,3),(2,3)],4)
=> 2 = 4 - 2
([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 4 - 2
([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 4 - 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 4 - 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 5 - 2
Description
The treewidth of a graph.
A graph has treewidth zero if and only if it has no edges. A connected graph has treewidth at most one if and only if it is a tree. A connected graph has treewidth at most two if and only if it is a series-parallel graph.
Matching statistic: St000536
(load all 7 compositions to match this statistic)
(load all 7 compositions to match this statistic)
Values
([],1)
=> 0 = 2 - 2
([],2)
=> 0 = 2 - 2
([(0,1)],2)
=> 1 = 3 - 2
([],3)
=> 0 = 2 - 2
([(1,2)],3)
=> 1 = 3 - 2
([(0,2),(1,2)],3)
=> 1 = 3 - 2
([(0,1),(0,2),(1,2)],3)
=> 2 = 4 - 2
([],4)
=> 0 = 2 - 2
([(2,3)],4)
=> 1 = 3 - 2
([(1,3),(2,3)],4)
=> 1 = 3 - 2
([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(0,3),(1,2)],4)
=> 1 = 3 - 2
([(0,3),(1,2),(2,3)],4)
=> 1 = 3 - 2
([(1,2),(1,3),(2,3)],4)
=> 2 = 4 - 2
([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 4 - 2
([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 4 - 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 4 - 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 5 - 2
Description
The pathwidth of a graph.
Matching statistic: St001277
(load all 7 compositions to match this statistic)
(load all 7 compositions to match this statistic)
Values
([],1)
=> 0 = 2 - 2
([],2)
=> 0 = 2 - 2
([(0,1)],2)
=> 1 = 3 - 2
([],3)
=> 0 = 2 - 2
([(1,2)],3)
=> 1 = 3 - 2
([(0,2),(1,2)],3)
=> 1 = 3 - 2
([(0,1),(0,2),(1,2)],3)
=> 2 = 4 - 2
([],4)
=> 0 = 2 - 2
([(2,3)],4)
=> 1 = 3 - 2
([(1,3),(2,3)],4)
=> 1 = 3 - 2
([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(0,3),(1,2)],4)
=> 1 = 3 - 2
([(0,3),(1,2),(2,3)],4)
=> 1 = 3 - 2
([(1,2),(1,3),(2,3)],4)
=> 2 = 4 - 2
([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 4 - 2
([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 4 - 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 4 - 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 5 - 2
Description
The degeneracy of a graph.
The degeneracy of a graph $G$ is the maximum of the minimum degrees of the (vertex induced) subgraphs of $G$.
Matching statistic: St001358
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
([],1)
=> 0 = 2 - 2
([],2)
=> 0 = 2 - 2
([(0,1)],2)
=> 1 = 3 - 2
([],3)
=> 0 = 2 - 2
([(1,2)],3)
=> 1 = 3 - 2
([(0,2),(1,2)],3)
=> 1 = 3 - 2
([(0,1),(0,2),(1,2)],3)
=> 2 = 4 - 2
([],4)
=> 0 = 2 - 2
([(2,3)],4)
=> 1 = 3 - 2
([(1,3),(2,3)],4)
=> 1 = 3 - 2
([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
([(0,3),(1,2)],4)
=> 1 = 3 - 2
([(0,3),(1,2),(2,3)],4)
=> 1 = 3 - 2
([(1,2),(1,3),(2,3)],4)
=> 2 = 4 - 2
([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 4 - 2
([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 4 - 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 4 - 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 5 - 2
Description
The largest degree of a regular subgraph of a graph.
For $k > 2$, it is an NP-complete problem to determine whether a graph has a $k$-regular subgraph, see [1].
Matching statistic: St000299
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
Values
([],1)
=> ([(0,1)],2)
=> 2
([],2)
=> ([(0,2),(1,2)],3)
=> 3
([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 4
([(1,2)],3)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 5
([(2,3)],4)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
([(1,3),(2,3)],4)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 3
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
Description
The number of nonisomorphic vertex-induced subtrees.
Matching statistic: St001318
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Values
([],1)
=> ([(0,1)],2)
=> 2
([],2)
=> ([(0,2),(1,2)],3)
=> 3
([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 4
([(1,2)],3)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 5
([(2,3)],4)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
([(1,3),(2,3)],4)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 3
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
Description
The number of vertices of the largest induced subforest with the same number of connected components of a graph.
The following 134 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001746The coalition number of a graph. St000388The number of orbits of vertices of a graph under automorphisms. St000918The 2-limited packing number of a graph. St001108The 2-dynamic chromatic number of a graph. St001116The game chromatic number of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001670The connected partition number of a graph. St001963The tree-depth of a graph. St000778The metric dimension of a graph. St001331The size of the minimal feedback vertex set. St001512The minimum rank of a graph. St000636The hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St000452The number of distinct eigenvalues of a graph. St000482The (zero)-forcing number of a graph. St000784The maximum of the length and the largest part of the integer partition. St001119The length of a shortest maximal path in a graph. St001315The dissociation number of a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001391The disjunction number of a graph. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St001180Number of indecomposable injective modules with projective dimension at most 1. St001486The number of corners of the ribbon associated with an integer composition. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St000015The number of peaks of a Dyck path. St000384The maximal part of the shifted composition of an integer partition. St000451The length of the longest pattern of the form k 1 2. St000453The number of distinct Laplacian eigenvalues of a graph. St000676The number of odd rises of a Dyck path. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. 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. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001530The depth of a Dyck path. St001674The number of vertices of the largest induced star graph in the graph. St001733The number of weak left to right maxima of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000053The number of valleys of the Dyck path. St000120The number of left tunnels of a Dyck path. St000141The maximum drop size of a permutation. St000160The multiplicity of the smallest part of a partition. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000331The number of upper interactions of a Dyck path. St000769The major index of a composition regarded as a word. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001185The number of indecomposable injective modules of grade at least 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. 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. St001274The number of indecomposable injective modules with projective dimension equal to two. 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. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001812The biclique partition number of a graph. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001330The hat guessing number of a graph. St000454The largest eigenvalue of a graph if it is integral. St001644The dimension of a graph. St000741The Colin de Verdière graph invariant. St001621The number of atoms of a lattice. St000776The maximal multiplicity of an eigenvalue in a graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000259The diameter of a connected graph. St000393The number of strictly increasing runs in 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. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001267The length of the Lyndon factorization of the binary word. St001504The sum of all indegrees of vertices with indegree at least two in the resolution quiver of a Nakayama algebra corresponding to the Dyck path. St000260The radius of a connected graph. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000144The pyramid weight of the Dyck path. St000806The semiperimeter of the associated bargraph. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in 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 St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St000455The second largest eigenvalue of a graph if it is integral. St001645The pebbling number of a connected graph. St001624The breadth of a lattice. St000735The last entry on the main diagonal of a standard tableau. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. 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. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. 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 $c_{n-1}$. St001019Sum of the projective dimensions of the simple modules in 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. 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. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. 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. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001838The number of nonempty primitive factors of a binary word. St001872The number of indecomposable injective modules with even projective dimension in the corresponding Nakayama algebra. St000264The girth of a graph, which is not a tree. St001060The distinguishing index of a graph. St001875The number of simple modules with projective dimension at most 1. 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 $eA$. St001118The acyclic chromatic index of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001651The Frankl number of a lattice. St000422The energy of a graph, if it is integral. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St001613The binary logarithm of the size of the center of a lattice. St001617The dimension of the space of valuations of a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St000302The determinant of the distance matrix of a connected graph. St000467The hyper-Wiener index of a connected graph. St001845The number of join irreducibles minus the rank of a lattice. St000438The position of the last up step in a Dyck path. St000981The length of the longest zigzag subpath. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001626The number of maximal proper sublattices of a lattice.
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