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: St001733The number of weak left to right maxima of a Dyck path. St001809The index of the step at the first peak of maximal height in a Dyck path. St000053The number of valleys of the Dyck path. St000211The rank of the set partition. St000234The number of global ascents of a permutation. St000439The position of the first down step of a Dyck path. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001176The size of a partition minus its first part. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St000010The length of the partition. St000093The cardinality of a maximal independent set of vertices of a graph. St000105The number of blocks in the set partition. St000167The number of leaves of an ordered tree. St000273The domination number of a graph. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000507The number of ascents of a standard tableau. St000544The cop number of a graph. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000808The number of up steps of the associated bargraph. St000916The packing number of a graph. St000971The smallest closer of a set partition. St001050The number of terminal closers of a set partition. St001058The breadth of the ordered tree. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001322The size of a minimal independent dominating set in a graph. St001339The irredundance number of a graph. St001363The Euler characteristic of a graph according to Knill. St000012The area of a Dyck path. St000157The number of descents of a standard tableau. St000340The number of non-final maximal constant sub-paths of length greater than one. St000521The number of distinct subtrees of an ordered tree. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001479The number of bridges of a graph. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001777The number of weak descents in an integer composition. St000444The length of the maximal rise of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000442The maximal area to the right of an up step of a Dyck path. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000502The number of successions of a set partitions. St000728The dimension of a set partition. St000874The position of the last double rise in a Dyck path. St000932The number of occurrences of the pattern UDU in a Dyck path. St000504The cardinality of the first block of a set partition. St000675The number of centered multitunnels of a Dyck path. St000925The number of topologically connected components of a set partition. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001062The maximal size of a block of a set partition. St000288The number of ones in a binary word. St000984The number of boxes below precisely one peak. St001498The normalised height of a Nakayama algebra with magnitude 1. St001580The acyclic chromatic number of a graph. St000272The treewidth of a graph. St000362The size of a minimal vertex cover of a graph. St000536The pathwidth of a graph. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St000308The height of the tree associated to a permutation. St001484The number of singletons of an integer partition. St000069The number of maximal elements of a poset. St000147The largest part of an integer partition. St001963The tree-depth of a graph. St000759The smallest missing part in an integer partition. St000912The number of maximal antichains in a poset. St000058The order of a permutation. St000445The number of rises of length 1 of a Dyck path. St000632The jump number of the poset. St000245The number of ascents of a permutation. St001461The number of topologically connected components of the chord diagram of a permutation. St000702The number of weak deficiencies of a permutation. St000533The minimum of the number of parts and the size of the first part of an integer partition. St001497The position of the largest weak excedence of a permutation. St001298The number of repeated entries in the Lehmer code of a permutation. St000654The first descent of a permutation. St000528The height of a poset. St000306The bounce count of a Dyck path. St000374The number of exclusive right-to-left minima of a permutation. St000703The number of deficiencies of a permutation. St000717The number of ordinal summands of a poset. St000906The length of the shortest maximal chain in a poset. St000643The size of the largest orbit of antichains under Panyushev complementation. St000783The side length of the largest staircase partition fitting into a partition. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000527The width of the poset. St000996The number of exclusive left-to-right maxima of a permutation. St000225Difference between largest and smallest parts in a partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St000159The number of distinct parts of the integer partition. 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. St001726The number of visible inversions of a permutation. St000809The reduced reflection length of the permutation. St000957The number of Bruhat lower covers of a permutation. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001432The order dimension of the partition. St000495The number of inversions of distance at most 2 of a permutation. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St000485The length of the longest cycle of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000470The number of runs in a permutation. St001489The maximum of the number of descents and the number of inverse descents. St000354The number of recoils of a permutation. St000795The mad of a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000831The number of indices that are either descents or recoils. St001061The number of indices that are both descents and recoils of a permutation. St000539The number of odd inversions of a permutation. St000653The last descent of a permutation. St000441The number of successions of a permutation. St000054The first entry of the permutation. St000451The length of the longest pattern of the form k 1 2. St000141The maximum drop size of a permutation. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000662The staircase size of the code of a permutation. St001397Number of pairs of incomparable elements in a finite poset. St000989The number of final rises of a permutation. St000028The number of stack-sorts needed to sort a permutation. St000203The number of external nodes of a binary tree. St000052The number of valleys of a Dyck path not on the x-axis. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St000740The last entry of a permutation. St000007The number of saliances of the permutation. St000546The number of global descents of a permutation. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St000446The disorder of a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000081The number of edges of a graph. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St000153The number of adjacent cycles of a permutation. St000214The number of adjacencies of a permutation. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000297The number of leading ones in a binary word. St000392The length of the longest run of ones in a binary word. St000720The size of the largest partition in the oscillating tableau corresponding to the perfect matching. St000982The length of the longest constant subword. St001372The length of a longest cyclic run of ones of a binary word. St000332The positive inversions of an alternating sign matrix. St000738The first entry in the last row of a standard tableau. St001046The maximal number of arcs nesting a given arc of a perfect matching. St000246The number of non-inversions of a permutation. St000067The inversion number of the alternating sign matrix. St000164The number of short pairs. St000291The number of descents of a binary word. St000390The number of runs of ones in a binary word. St000292The number of ascents of a binary word. St000237The number of small exceedances. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St000843The decomposition number of a perfect matching. St000542The number of left-to-right-minima of a permutation. St000366The number of double descents of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St000443The number of long tunnels of a Dyck path. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. 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. St000015The number of peaks of a Dyck path. St000056The decomposition (or block) number of a permutation. St000240The number of indices that are not small excedances. St000325The width of the tree associated to a permutation. St000991The number of right-to-left minima of a permutation. 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. 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. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St000021The number of descents of a permutation. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000120The number of left tunnels of a Dyck path. St000168The number of internal nodes of an ordered tree. St000238The number of indices that are not small weak excedances. St000316The number of non-left-to-right-maxima of a permutation. St000331The number of upper interactions of a Dyck path. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. 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. St001233The number of indecomposable 2-dimensional modules with projective dimension one. 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. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St000062The length of the longest increasing subsequence of the permutation. St000084The number of subtrees. St000166The depth minus 1 of an ordered tree. St000213The number of weak exceedances (also weak excedences) of a permutation. St000239The number of small weak excedances. St000287The number of connected components of a graph. St000314The number of left-to-right-maxima of a permutation. St000328The maximum number of child nodes in a tree. St000990The first ascent of a permutation. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001828The Euler characteristic of a graph. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St000004The major index of a permutation. St000080The rank of the poset. St000094The depth of an ordered tree. St000155The number of exceedances (also excedences) of a permutation. St000204The number of internal nodes of a binary tree. St000224The sorting index of a permutation. St000305The inverse major index of a permutation. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000336The leg major index of a standard tableau. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000794The mak of a permutation. St000931The number of occurrences of the pattern UUU in a Dyck path. St001077The prefix exchange distance of a permutation. St001115The number of even descents of a permutation. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St001180Number of indecomposable injective modules with projective dimension at most 1. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001427The number of descents of a signed permutation. St001428The number of B-inversions of a signed permutation. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001869The maximum cut size of a graph. 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 $c_{n-1}$. 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. 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. St001480The number of simple summands of the module J^2/J^3. St000083The number of left oriented leafs of a binary tree except the first one. St000216The absolute length of a permutation. St000061The number of nodes on the left branch of a binary tree. St001812The biclique partition number of a graph. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000365The number of double ascents of a permutation. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St000840The number of closers smaller than the largest opener in a perfect matching. St000731The number of double exceedences of a permutation. St000746The number of pairs with odd minimum in a perfect matching. St000223The number of nestings in the permutation. St000022The number of fixed points of a permutation. St000119The number of occurrences of the pattern 321 in a permutation. St000123The difference in Coxeter length of a permutation and its image under the Simion-Schmidt map. St000356The number of occurrences of the pattern 13-2. St001083The number of boxed occurrences of 132 in a permutation. St000711The number of big exceedences of a permutation. St001082The number of boxed occurrences of 123 in a permutation. St000039The number of crossings of a permutation. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St000156The Denert index of a permutation. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000200The row of the unique '1' in the last column of the alternating sign matrix. St000619The number of cyclic descents of a permutation. St001589The nesting number of a perfect matching. St000034The maximum defect over any reduced expression for a permutation and any subexpression. St000144The pyramid weight of the Dyck path. St000242The number of indices that are not cyclical small weak excedances. St000317The cycle descent number of a permutation. St000358The number of occurrences of the pattern 31-2. St000732The number of double deficiencies of a permutation. St000802The number of occurrences of the vincular pattern |321 in a permutation. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001089Number of indecomposable projective non-injective modules minus the number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001164Number of indecomposable injective modules whose socle has projective dimension at most g-1 (g the global dimension) minus the number of indecomposable projective-injective modules. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001231The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. St001234The number of indecomposable three dimensional modules with projective dimension one. St001411The number of patterns 321 or 3412 in a permutation. St001552The number of inversions between excedances and fixed points of a permutation. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001727The number of invisible inversions of a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001810The number of fixed points of a permutation smaller than its largest moved point. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. St001668The number of points of the poset minus the width of the poset. St000327The number of cover relations in a poset. St001948The number of augmented double ascents of a permutation. St001820The size of the image of the pop stack sorting operator. St001330The hat guessing number of a graph. St001769The reflection length of a signed permutation. St001861The number of Bruhat lower covers of a permutation. St001894The depth of a signed permutation. St001896The number of right descents of a signed permutations. St001889The size of the connectivity set of a signed permutation. St000896The number of zeros on the main diagonal of an alternating sign matrix. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St001596The number of two-by-two squares inside a skew partition. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001462The number of factors of a standard tableaux under concatenation. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001712The number of natural descents of a standard Young tableau. St001811The Castelnuovo-Mumford regularity of a permutation. St001905The number of preferred parking spots in a parking function less than the index of the car. St001935The number of ascents in a parking function. St001946The number of descents in a parking function. St001960The number of descents of a permutation minus one if its first entry is not one. 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. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001626The number of maximal proper sublattices of a lattice. St001720The minimal length of a chain of small intervals in a lattice.