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Your data matches 128 different statistics following compositions of up to 3 maps.
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Matching statistic: St001093
(load all 2 compositions to match this statistic)
(load all 2 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)
=> 3 = 4 - 1
([(0,1),(0,2),(1,2)],3)
=> 2 = 3 - 1
([],4)
=> 1 = 2 - 1
([(2,3)],4)
=> 2 = 3 - 1
([(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,3),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,3),(1,2)],4)
=> 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
=> 4 = 5 - 1
([(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 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)
=> 2 = 3 - 1
Description
The detour number of a graph.
This is the number of vertices in a longest induced path in a graph.
Note that [1] defines the detour number as the number of edges in a longest induced path, which is unsuitable for the empty graph.
Matching statistic: St001116
(load all 3 compositions to match this statistic)
(load all 3 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)
=> 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 game chromatic number of a graph.
Two players, Alice and Bob, take turns colouring properly any uncolored vertex of the graph. Alice begins. If it is not possible for either player to colour a vertex, then Bob wins. If the graph is completely colored, Alice wins.
The game chromatic number is the smallest number of colours such that Alice has a winning strategy.
Matching statistic: St001670
(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)
=> 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)
=> 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 connected partition number of a graph.
This is the maximal number of blocks of a set partition $P$ of the set of vertices of a graph such that contracting each block of $P$ to a single vertex yields a clique.
Also called the pseudoachromatic number of a graph. This is the largest $n$ such that there exists a (not necessarily proper) $n$-coloring of the graph so that every two distinct colors are adjacent.
Matching statistic: St001674
(load all 4 compositions to match this statistic)
(load all 4 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)
=> 3 = 4 - 1
([(0,1),(0,2),(1,2)],3)
=> 2 = 3 - 1
([],4)
=> 1 = 2 - 1
([(2,3)],4)
=> 2 = 3 - 1
([(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,3),(1,3),(2,3)],4)
=> 4 = 5 - 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)
=> 2 = 3 - 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)
=> 2 = 3 - 1
Description
The number of vertices of the largest induced star graph in the graph.
Matching statistic: St001883
(load all 3 compositions to match this statistic)
(load all 3 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)
=> 3 = 4 - 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 mutual visibility number of a graph.
This is the largest cardinality of a subset $P$ of vertices of a graph $G$, such that for each pair of vertices in $P$ there is a shortest path in $G$ which contains no other point in $P$.
In particular, the mutual visibility number of the disjoint union of two graphs is the maximum of their mutual visibility numbers.
Matching statistic: St001963
(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)
=> 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)
=> 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 tree-depth of a graph.
The tree-depth $\operatorname{td}(G)$ of a graph $G$ whose connected components are $G_1,\ldots,G_p$ is recursively defined as
$$\operatorname{td}(G)=\begin{cases} 1, & \text{if }|G|=1\\ 1 + \min_{v\in V} \operatorname{td}(G-v), & \text{if } p=1 \text{ and } |G| > 1\\ \max_{i=1}^p \operatorname{td}(G_i), & \text{otherwise} \end{cases}$$
Nešetřil and Ossona de Mendez [2] proved that the tree-depth of a connected graph is equal to its minimum elimination tree height and its centered chromatic number (fewest colors needed for a vertex coloring where every connected induced subgraph has a color that appears exactly once).
Tree-depth is strictly greater than [[St000536|pathwidth]]. A [[St001120|longest path]] in $G$ has at least $\operatorname{td}(G)$ vertices [3].
Matching statistic: St001270
(load all 2 compositions to match this statistic)
(load all 2 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)
=> 2 = 4 - 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 bandwidth of a graph.
The bandwidth of a graph is the smallest number $k$ such that the vertices of the graph can be
ordered as $v_1,\dots,v_n$ with $k \cdot d(v_i,v_j) \geq |i-j|$.
We adopt the convention that the singleton graph has bandwidth $0$, consistent with the bandwith of the complete graph on $n$ vertices having bandwidth $n-1$, but in contrast to any path graph on more than one vertex having bandwidth $1$. The bandwidth of a disconnected graph is the maximum of the bandwidths of the connected components.
Matching statistic: St001644
(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)
=> 2 = 4 - 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 dimension of a graph.
The dimension of a graph is the least integer $n$ such that there exists a representation of the graph in the Euclidean space of dimension $n$ with all vertices distinct and all edges having unit length. Edges are allowed to intersect, however.
Matching statistic: St001812
(load all 11 compositions to match this statistic)
(load all 11 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)
=> 2 = 4 - 2
([(0,3),(1,2),(2,3)],4)
=> 2 = 4 - 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)
=> 1 = 3 - 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 biclique partition number of a graph.
The biclique partition number of a graph is the minimum number of pairwise edge disjoint complete bipartite subgraphs so that each edge belongs to exactly one of them. A theorem of Graham and Pollak [1] asserts that the complete graph $K_n$ has biclique partition number $n - 1$.
Matching statistic: St001962
(load all 2 compositions to match this statistic)
(load all 2 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)
=> 2 = 4 - 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 proper pathwidth of a graph.
The proper pathwidth $\operatorname{ppw}(G)$ was introduced in [1] as the minimum width of a proper-path-decomposition. Barioli et al. [2] showed that if $G$ has at least one edge, then $\operatorname{ppw}(G)$ is the minimum $k$ for which $G$ is a minor of the Cartesian product $K_k \square P$ of a complete graph on $k$ vertices with a path; and further that $\operatorname{ppw}(G)$ is the minor monotone floor $\lfloor \operatorname{Z} \rfloor(G) := \min\{\operatorname{Z}(H) \mid G \preceq H\}$ of the [[St000482|zero forcing number]] $\operatorname{Z}(G)$. It can be shown [3, Corollary 9.130] that only the spanning supergraphs need to be considered for $H$ in this definition, i.e. $\lfloor \operatorname{Z} \rfloor(G) = \min\{\operatorname{Z}(H) \mid G \le H,\; V(H) = V(G)\}$.
The minimum degree $\delta$, treewidth $\operatorname{tw}$, and pathwidth $\operatorname{pw}$ satisfy
$$\delta \le \operatorname{tw} \le \operatorname{pw} \le \operatorname{ppw} = \lfloor \operatorname{Z} \rfloor \le \operatorname{pw} + 1.$$
Note that [4] uses a different notion of proper pathwidth, which is equal to bandwidth.
The following 118 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001321The number of vertices of the largest induced subforest of a graph. St000482The (zero)-forcing number of a graph. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000776The maximal multiplicity of an eigenvalue in a graph. St001315The dissociation number of a graph. St000362The size of a minimal vertex cover of a graph. St001345The Hamming dimension of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St001110The 3-dynamic chromatic number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St000382The first part of an integer composition. St000778The metric dimension of a graph. St001642The Prague dimension of a graph. St001638The book thickness of a graph. St000439The position of the first down step of a Dyck path. St001180Number of indecomposable injective modules with projective dimension at most 1. 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. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St000013The height of a Dyck path. St000025The number of initial rises of a Dyck path. St000383The last part of an integer composition. St000443The number of long tunnels of a Dyck path. St000451The length of the longest pattern of the form k 1 2. St000453The number of distinct Laplacian eigenvalues of a graph. St000459The hook length of the base cell of a partition. St000676The number of odd rises of a Dyck path. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000765The number of weak records in an integer composition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001210Gives the maximal vector space dimension of the first Ext-group between an indecomposable module X and the regular module A, when A is the Nakayama algebra corresponding to the Dyck path. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama 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. St001809The index of the step at the first peak of maximal height in a Dyck path. St000024The number of double up and double down steps of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000120The number of left tunnels of a Dyck path. 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. St000742The number of big ascents of a permutation after prepending zero. St000766The number of inversions of an integer composition. 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. 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 $A$. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001233The number of indecomposable 2-dimensional modules with projective dimension one. 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. St000444The length of the maximal 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. St000442The maximal area to the right of an up step of a Dyck path. St000874The position of the last double rise in a Dyck path. St001418Half of the global dimension of the 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. St000741The Colin de Verdière graph invariant. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000806The semiperimeter of the associated bargraph. 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 $c_{n-1}$. 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. St000259The diameter 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. St001179Number of indecomposable injective modules with projective dimension at most 2 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. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000455The second largest eigenvalue of a graph if it is integral. St001645The pebbling number of a connected graph. St001621The number of atoms of a lattice. St001624The breadth of a lattice. St000735The last entry on the main diagonal of a standard tableau. St000260The radius 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. St001570The minimal number of edges to add to make a graph Hamiltonian. 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. 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. 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. St001065Number of indecomposable reflexive modules 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. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama 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. 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 $eA$. St000264The girth of a graph, which is not a tree. St001118The acyclic chromatic index of a graph. 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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