The bounce statistic of a Dyck path.

The number of touch points of a Dyck path.

The height of a Dyck path.

The number of parking functions supported by a Dyck path.

The number of peaks of a Dyck path.

The number of double up and double down steps of a Dyck path.

The number of initial rises of a Dyck path.

The position of the first return of a Dyck path.

The major index of a Dyck path.

The number of elements smaller than the given Dyck path in the Tamari Order.

The product of the heights of the descending steps of a Dyck path.

The number of valleys of a Dyck path not on the x-axis.

The number of valleys of the Dyck path.

The number of alternating sign matrices for a given Dyck path.

The number of centered tunnels of a Dyck path.

The number of left tunnels of a Dyck path.

The pyramid weight of the Dyck path.

The bounce count of a Dyck path.

The number of evenly positioned ascents of the Dyck path, with the initial positi....

The number of upper interactions of a Dyck path.

The difference of lower and upper interactions.

The number of non-final maximal sub-paths of length greater than one.

The dinv deficit of a Dyck path.

The bounce deficit of a Dyck path.

The number of factors DDU in a Dyck path.

The sum of the heights of the peaks of a Dyck path minus the number of peaks.

The sum of the heights of the peaks of a Dyck path.

The number of Dyck paths that are weakly below a Dyck path.

The number of Dyck paths that are weakly above the Dyck path, except for the path....

The number of Dyck paths that are weakly above a Dyck path.

The number of Dyck paths that are weakly below a Dyck path, except for the path i....

The position of the last up step in a Dyck path.

The position of the first down step of a Dyck path.

The maximal area to the right of an up step of a Dyck path.

The number of long tunnels of a Dyck path.

The length of the maximal rise of a Dyck path.

The number of rises of length 1 of a Dyck path.

The sum of the semi-lengths of tunnels before a valley of a Dyck path.

The number of global maxima of a Dyck path.

The sum of the areas of the rectangles formed by two consecutive peaks and the va....

The length of the minimal rise of a Dyck path.

The number of rises of length 2 of a Dyck path.

The number of rises of length at least 2 of a Dyck path.

The number of rises of length at least 3 of a Dyck path.

The number of rises of length 3 of a Dyck path.

The number of hills of a Dyck path.

The number of centered multitunnels of a Dyck path.

The number of odd rises of a Dyck path.

The number of up steps after the last double rise of a Dyck path.

The number of points below the Dyck path such that the diagonal to the north-east....

The global dimension of the LNakayama algebra associated to a Dyck path.

The dominant dimension of the LNakayama algebra associated to a Dyck path.

The finitistic dominant dimension of a Dyck path.

The dimension of $Hom(I,P)$ for the LNakayama algebra of a Dyck path.

The global dimension minus the dominant dimension of the LNakayama algebra associ....

The maximal n such that the minimal generator-cogenerator module in the LNakayama....

The number of pairs of centered tunnels, one strictly containing the other, of a ....

The number of pairs of left tunnels, one strictly containing the other, of a Dyck....

The position of the last double rise in a Dyck path.

The logarithmic height of a Dyck path.

The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver.....

The number of occurrences of the pattern UUU in a Dyck path.

The number of occurrences of the pattern UDU in a Dyck path.

The sum of the skew hook positions in a Dyck path.

The major index of a Dyck path according to Zhao and Zhong.

Gives the number of generalised tilting modules of the corresponding LNakayama al....

Number of tilting modules of the corresponding LNakayama algebra, where a tilting....

The dimension of $Ext^{1}(D(A),A)$ of the corresponding LNakayama algebra.

Gives the number of irreducible factors of the Coxeter polynomial of the Dyck pat....

The largest degree of an irreducible factor of the Coxeter polynomial of the Dyck....

Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$.

Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama a....

Gives the dimension of Ext^g(D(A),A) of the corresponding LNakayama algebra, when....

The sum of the dimension of Ext^i(D(A),A) for i=1,.

Number of peaks minus the global dimension of the corresponding LNakayama algebra....

The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra....

We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dy....

We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dy....

Number of peaks minus the dominant dimension of the corresponding LNakayama algeb....

The sum of the positions of double up-steps of a Dyck path.

MacMahon's equal index of a Dyck path.

The sum of the positions of double down-steps of a Dyck path.

Half of MacMahon's equal index of a Dyck path.

The number of boxes weakly below the path and above the diagonal that lie below a....

The length of the longest zigzag subpath.

The number of boxes below precisely one peak.

Number of indecomposable projective modules with injective dimension smaller than....

Number of indecomposable projective module with injective dimension equal to the ....

Number of indecomposable modules with projective dimension equal to the global di....

The number of indecomposable modules with projective and injective dimension equa....

Number of indecomposable modules with projective and injective dimension at most ....

The number of indecomposable modules with projective dimension at most 1 in the N....

Number of isimple modules with projective dimension equal to the global dimension....

Number of simple modules with projective dimension 1 in the Nakayama algebra corr....

Number of indecomposable injective modules with projective dimension 1 in the Nak....

Number of indecomposable injective modules with projective dimension g when g is ....

Number of indecomposable injective modules with projective dimension g-1 when g i....

Number of simple modules of projective dimension 2 in the Nakayama algebra corres....

Number of simple modules with projective dimension at most 2 in the Nakayama alge....

Number of indecomposable injective modules with codominant dimension equal to the....

Number of indecomposable injective modules with codominant dimension equal to the....

Number of indecomposable injective modules with codominant dimension equal to one....

Number of indecomosable injective modules with codominant dimension at most 1 in ....

Number of indecomposable injective modules with projective dimension equal to the....

Sum of projective dimension of the indecomposable injective modules of the Nakaya....

Sum of the projective dimensions of the simple modules in the Nakayama algebra co....

Sum of the codominant dimensions of the non-projective indecomposable injective m....

Sum of the differences between projective and codominant dimension of the non-pro....

Number of simple modules with projective dimension 3 in the Nakayama algebra corr....

Number of simple modules with projective dimension at most 3 in the Nakayama alge....

Maximum of dominant dimensions of the simple modules in the Nakayama algebra corr....

Number of simple modules with projective dimension 4 in the Nakayama algebra corr....

The maximum of the projective dimensions of the indecomposable non-projective inj....

Number of simple modules with projective dimension equal to injective dimension i....

Number of simple modules with injective dimension equal to the dominant dimension....

The height of the bicoloured Motzkin path associated with the Dyck path.

The number of horizontal steps in the bicoloured Motzkin path associated with the....

The normalized area of the parallelogram polyomino associated with the Dyck path.....

The area of the parallelogram polyomino associated with the Dyck path.

The convexity degree of the parallelogram polyomino associated with the Dyck path....

The number of inner corners of the parallelogram polyomino associated with the Dy....

The number of inner corners of the upper path of the parallelogram polyomino asso....

The minimal height of a column in the parallelogram polyomino associated with the....

The maximal height of a column in the parallelogram polyomino associated with a D....

Numbers of 3-torsionfree simple modules in the corresponding Nakayama algebra.

Number of simple modules in the corresponding Nakayama algebra that are 3-syzygy ....

Number of indecomposable reflexive modules in the corresponding Nakayama algebra.....

The number of simple reflexive modules in the corresponding Nakayama algebra.

The number of simple modules of dominant dimension at least two in the correspond....

Number of torsionless simple modules in the corresponding Nakayama algebra.

Number of indecomposable projective non-injective modules with dominant dimension....

Number of indecomposable projective non-injective modules minus the number of ind....