Your data matches 372 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001815
St001815: Posets ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
([],1)
=> 1 = 0 + 1
([],2)
=> 3 = 2 + 1
([(0,1)],2)
=> 2 = 1 + 1
Description
The number of order preserving surjections from a poset to a total order.
Matching statistic: St000070
St000070: Posets ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
([],1)
=> 2 = 0 + 2
([],2)
=> 4 = 2 + 2
([(0,1)],2)
=> 3 = 1 + 2
Description
The number of antichains in a poset. An antichain in a poset $P$ is a subset of elements of $P$ which are pairwise incomparable. An order ideal is a subset $I$ of $P$ such that $a\in I$ and $b \leq_P a$ implies $b \in I$. Since there is a one-to-one correspondence between antichains and order ideals, this statistic is also the number of order ideals in a poset.
Matching statistic: St000104
St000104: Posets ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
([],1)
=> 2 = 0 + 2
([],2)
=> 4 = 2 + 2
([(0,1)],2)
=> 3 = 1 + 2
Description
The number of facets in the order polytope of this poset.
Matching statistic: St000151
St000151: Posets ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
([],1)
=> 2 = 0 + 2
([],2)
=> 4 = 2 + 2
([(0,1)],2)
=> 3 = 1 + 2
Description
The number of facets in the chain polytope of the poset.
Matching statistic: St000180
St000180: Posets ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
([],1)
=> 2 = 0 + 2
([],2)
=> 3 = 1 + 2
([(0,1)],2)
=> 4 = 2 + 2
Description
The number of chains of a poset.
Mp00306: Posets rowmotion cycle typeInteger partitions
St000137: Integer partitions ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
([],1)
=> [2]
=> 0
([],2)
=> [2,2]
=> 2
([(0,1)],2)
=> [3]
=> 1
Description
The Grundy value of an integer partition. Consider the two-player game on an integer partition. In each move, a player removes either a box, or a 2x2-configuration of boxes such that the resulting diagram is still a partition. The first player that cannot move lose. This happens exactly when the empty partition is reached. The grundy value of an integer partition is defined as the grundy value of this two-player game as defined in [1]. This game was described to me during Norcom 2013, by Urban Larsson, and it seems to be quite difficult to give a good description of the partitions with Grundy value 0.
Matching statistic: St000811
Mp00306: Posets rowmotion cycle typeInteger partitions
St000811: Integer partitions ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
([],1)
=> [2]
=> 0
([],2)
=> [2,2]
=> 2
([(0,1)],2)
=> [3]
=> 1
Description
The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to Schur symmetric functions. For example, $p_{22} = s_{1111} - s_{211} + 2s_{22} - s_{31} + s_4$, so the statistic on the partition $22$ is 2. This is also the sum of the character values at the given conjugacy class over all irreducible characters of the symmetric group. [2] For a permutation $\pi$ of given cycle type, this is also the number of permutations whose square equals $\pi$. [2]
Matching statistic: St001391
Mp00074: Posets to graphGraphs
St001391: Graphs ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
([],1)
=> ([],1)
=> 0
([],2)
=> ([],2)
=> 2
([(0,1)],2)
=> ([(0,1)],2)
=> 1
Description
The disjunction number of a graph. Let $V_n$ be the power set of $\{1,\dots,n\}$ and let $E_n=\{(a,b)| a,b\in V_n, a\neq b, a\cap b=\emptyset\}$. Then the disjunction number of a graph $G$ is the smallest integer $n$ such that $(V_n, E_n)$ has an induced subgraph isomorphic to $G$.
Matching statistic: St001613
Mp00282: Posets Dedekind-MacNeille completionLattices
St001613: Lattices ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
([],1)
=> ([],1)
=> 0
([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,1)],2)
=> ([(0,1)],2)
=> 1
Description
The binary logarithm of the size of the center of a lattice. An element of a lattice is central if it is neutral and has a complement. The subposet induced by central elements is a Boolean lattice.
Mp00282: Posets Dedekind-MacNeille completionLattices
St001615: Lattices ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
([],1)
=> ([],1)
=> 0
([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,1)],2)
=> ([(0,1)],2)
=> 1
Description
The number of join prime elements of a lattice. An element $x$ of a lattice $L$ is join-prime (or coprime) if $x \leq a \vee b$ implies $x \leq a$ or $x \leq b$ for every $a, b \in L$.
The following 362 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001617The dimension of the space of valuations of a lattice. St001621The number of atoms of a lattice. St001622The number of join-irreducible elements of a lattice. St001623The number of doubly irreducible elements of a lattice. St000182The number of permutations whose cycle type is the given integer partition. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000812The sum of the entries in the column specified by the partition of the change of basis matrix from complete homogeneous symmetric functions to monomial symmetric functions. St000867The sum of the hook lengths in the first row of an integer partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St001441The number of non-empty connected induced subgraphs of a graph. St001625The Möbius invariant of a lattice. St000228The size of a partition. St000300The number of independent sets of vertices of a graph. St000301The number of facets of the stable set polytope of a graph. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000708The product of the parts of an integer partition. St000815The number of semistandard Young tableaux of partition weight of given shape. St000933The number of multipartitions of sizes given by an integer partition. St001279The sum of the parts of an integer partition that are at least two. St001527The cyclic permutation representation number of an integer partition. St001616The number of neutral elements in a lattice. St001834The number of non-isomorphic minors of a graph. St001619The number of non-isomorphic sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St000080The rank of the poset. St000149The number of cells of the partition whose leg is zero and arm is odd. St000340The number of non-final maximal constant sub-paths of length greater than one. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St000934The 2-degree of an integer partition. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St000012The area of a Dyck path. St000081The number of edges of a graph. St000185The weighted size of a partition. St000271The chromatic index of a graph. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000528The height of a poset. St000675The number of centered multitunnels of a Dyck path. St000681The Grundy value of Chomp on Ferrers diagrams. St000683The number of points below the Dyck path such that the diagonal to the north-east hits the path between two down steps, and the diagonal to the north-west hits the path between two up steps. St000912The number of maximal antichains in a poset. St000928The sum of the coefficients of the character polynomial of an integer partition. St000984The number of boxes below precisely one peak. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001111The weak 2-dynamic chromatic number of a graph. St001112The 3-weak dynamic number of a graph. St001117The game chromatic index of a graph. St001118The acyclic chromatic index of a graph. 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. St001242The toal dimension of certain Sn modules determined by LLT polynomials associated with a Dyck path. St001243The sum of coefficients in the Schur basis of certain LLT polynomials associated with a Dyck path. St001254The vector space dimension of the first extension-group between A/soc(A) and J when A is the corresponding Nakayama algebra with Jacobson radical J. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001343The dimension of the reduced incidence algebra of a poset. St001345The Hamming dimension of a graph. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001649The length of a longest trail in a graph. St001827The number of two-component spanning forests of a graph. St001961The sum of the greatest common divisors of all pairs of parts. St000086The number of subgraphs. St000087The number of induced subgraphs. St000184The size of the centralizer of any permutation of given cycle type. St000189The number of elements in the poset. St000293The number of inversions of a binary word. St000384The maximal part of the shifted composition of an integer partition. St000459The hook length of the base cell of a partition. St000460The hook length of the last cell along the main diagonal of an integer partition. St000468The Hosoya index of a graph. St000531The leading coefficient of the rook polynomial of an integer partition. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000656The number of cuts of a poset. St000784The maximum of the length and the largest part of the integer partition. St000814The sum of the entries in the column specified by the partition of the change of basis matrix from elementary symmetric functions to Schur symmetric functions. St000827The decimal representation of a binary word with a leading 1. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000915The Ore degree of a graph. St000926The clique-coclique number of a graph. St001034The area of the parallelogram polyomino associated with the Dyck path. St001180Number of indecomposable injective modules with projective dimension at most 1. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001249Sum of the odd parts of a partition. St001259The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001360The number of covering relations in Young's lattice below a partition. St001492The number of simple modules that do not appear in the socle of the regular module or have no nontrivial selfextensions with the regular module in the corresponding Nakayama algebra. 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. St001614The cyclic permutation representation number of a skew partition. St001645The pebbling number of a connected graph. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001717The largest size of an interval in a poset. St001782The order of rowmotion on the set of order ideals of a poset. St001808The box weight or horizontal decoration of a Dyck path. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001959The product of the heights of the peaks of a Dyck path. St000063The number of linear extensions of a certain poset defined for an integer partition. St000108The number of partitions contained in the given partition. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000438The position of the last up step in a Dyck path. St000532The total number of rook placements on a Ferrers board. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001400The total number of Littlewood-Richardson tableaux of given shape. St001814The number of partitions interlacing the given partition. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001838The number of nonempty primitive factors of a binary word. St000004The major index of a permutation. St000005The bounce statistic of a Dyck path. St000006The dinv of a Dyck path. St000024The number of double up and double down steps of a Dyck path. St000053The number of valleys of the Dyck path. St000117The number of centered tunnels of a Dyck path. St000120The number of left tunnels of a Dyck path. St000133The "bounce" of a permutation. St000148The number of odd parts of a partition. St000154The sum of the descent bottoms of a permutation. St000156The Denert index of a permutation. St000289The decimal representation of a binary word. St000290The major index of a binary word. St000304The load of a permutation. St000305The inverse major index of a permutation. St000306The bounce count of a Dyck path. 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. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000389The number of runs of ones of odd length in a binary word. St000391The sum of the positions of the ones in a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000442The maximal area to the right of an up step of a Dyck path. St000446The disorder of a permutation. St000448The number of pairs of vertices of a graph with distance 2. St000461The rix statistic of a permutation. St000472The sum of the ascent bottoms of a permutation. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000549The number of odd partial sums of an integer partition. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000646The number of big ascents of a permutation. St000653The last descent of a permutation. St000663The number of right floats of a permutation. St000682The Grundy value of Welter's game on a binary word. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000691The number of changes of a binary word. St000742The number of big ascents of a permutation after prepending zero. St000792The Grundy value for the game of ruler on a binary word. St000793The length of the longest partition in the vacillating tableau corresponding to a set partition. St000794The mak of a permutation. St000796The stat' of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000833The comajor index of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St000874The position of the last double rise in a Dyck path. St000932The number of occurrences of the pattern UDU in a Dyck path. St000947The major index east count of a Dyck path. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St000961The shifted major index of a permutation. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001010Number of indecomposable injective modules with projective dimension g-1 when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001161The major index north count of a 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. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001205The number of non-simple indecomposable projective-injective modules of the algebra $eAe$ in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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. St001223Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical 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. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001273The projective dimension of the first term in an injective coresolution of the regular module. 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. 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. St001347The number of pairs of vertices of a graph having the same neighbourhood. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001424The number of distinct squares in a binary word. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001480The number of simple summands of the module J^2/J^3. St001485The modular major index of a binary word. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 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. St001524The degree of symmetry of a binary word. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001671Haglund's hag of a permutation. 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. St001759The Rajchgot index of a permutation. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St001799The number of proper separations of a graph. St001910The height of the middle non-run of a Dyck path. St001930The weak major index of a binary word. St000008The major index of the composition. St000013The height of a Dyck path. St000015The number of peaks of a Dyck path. St000020The rank of the permutation. St000025The number of initial rises of a Dyck path. St000026The position of the first return of a Dyck path. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000059The inversion number of a standard tableau as defined by Haglund and Stevens. St000169The cocharge of a standard tableau. St000224The sorting index of a permutation. St000231Sum of the maximal elements of the blocks of a set partition. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000330The (standard) major index of a standard tableau. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000336The leg major index of a standard tableau. St000398The sum of the depths of the vertices (or total internal path length) of a binary tree. St000400The path length of an ordered tree. St000420The number of Dyck paths that are weakly above a Dyck path. St000443The number of long tunnels of a Dyck path. St000444The length of the maximal rise of a Dyck path. St000507The number of ascents of a standard tableau. St000509The diagonal index (content) of a partition. St000519The largest length of a factor maximising the subword complexity. St000617The number of global maxima of a Dyck path. St000626The minimal period of a binary word. St000638The number of up-down runs of a permutation. St000651The maximal size of a rise in a permutation. St000652The maximal difference between successive positions of a permutation. St000676The number of odd rises of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000734The last entry in the first row of a standard tableau. St000740The last entry of a permutation. St000795The mad of a permutation. St000841The largest opener of a perfect matching. St000878The number of ones minus the number of zeros of a binary word. St000922The minimal number such that all substrings of this length are unique. St000946The sum of the skew hook positions in a Dyck path. St000952Gives the number of irreducible factors of the Coxeter polynomial of the Dyck path over the rational numbers. St000964Gives the dimension of Ext^g(D(A),A) of the corresponding LNakayama algebra, when g denotes the global dimension of that algebra. St000965The sum of the dimension of Ext^i(D(A),A) for i=1,. St000983The length of the longest alternating subword. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001009Number of indecomposable injective modules with projective dimension g when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. 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. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001203We associate to 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 Dyck path as follows: 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. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001285The number of primes in the column sums of the two line notation of a permutation. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. 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. St001313The number of Dyck paths above the lattice path given by a binary word. St001346The number of parking functions that give the same permutation. St001352The number of internal nodes in the modular decomposition of a graph. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001481The minimal height of a peak of a Dyck path. St001497The position of the largest weak excedence of a permutation. St001500The global dimension of magnitude 1 Nakayama algebras. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001530The depth of a Dyck path. St001697The shifted natural comajor index of a standard Young tableau. St001733The number of weak left to right maxima of a Dyck path. St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. St001809The index of the step at the first peak of maximal height in a Dyck path. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St001917The order of toric promotion on the set of labellings of a graph. St001956The comajor index for set-valued two-row standard Young tableaux. St001957The number of Hasse diagrams with a given underlying undirected graph. St000027The major index of a Dyck path. St000030The sum of the descent differences of a permutations. St000144The pyramid weight of the Dyck path. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000294The number of distinct factors of a binary word. St000321The number of integer partitions of n that are dominated by an integer partition. St000393The number of strictly increasing runs in a binary word. St000395The sum of the heights of the peaks of a Dyck path. St000439The position of the first down step of a Dyck path. St000479The Ramsey number of a graph. St000518The number of distinct subsequences in a binary word. St000625The sum of the minimal distances to a greater element. St000636The hull number of a graph. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St000951The dimension of $Ext^{1}(D(A),A)$ 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 $c_{n-1}$. St000979Half of MacMahon's equal index of a Dyck path. St000981The length of the longest zigzag subpath. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001018Sum of projective dimension of the indecomposable injective modules of 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. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. 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. St001267The length of the Lyndon factorization of the binary word. St001315The dissociation number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001342The number of vertices in the center of a graph. St001379The number of inversions plus the major index of a permutation. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001672The restrained domination number of a graph. St001721The degree of a binary word. St001725The harmonious chromatic number of a graph. St001746The coalition number of a graph. St001929The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path. 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. 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. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001872The number of indecomposable injective modules with even projective dimension in the corresponding Nakayama algebra. St001875The number of simple modules with projective dimension at most 1. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St001437The flex of a binary word. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001138The number of indecomposable modules with projective dimension or injective dimension at most one in the corresponding Nakayama algebra.