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, with the initial position equal to 1.

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 a Dyck path, except for the path i....

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.

Mp00007
Alternating sign matrices ⟶ Dyck paths

to Dyck path

to Dyck path: up step, left tree, down step, right tree

to Tamari-corresponding Dyck path

to non-crossing permutation

to 321-avoiding permutation

to 132-avoiding permutation

Mp00027
Dyck paths ⟶ Integer partitions

to partition

to Tamari-corresponding binary tree

to 312-avoiding permutation

Mp00033
Dyck paths ⟶ Standard tableaux

to two-row standard tableau

to binary tree: up step, left tree, down step, right tree

Mp00035
Dyck paths ⟶ Alternating sign matrices

to alternating sign matrix

Mp00043
Integer partitions ⟶ Dyck paths

to Dyck path

Mp00056
Parking functions ⟶ Dyck paths

to Dyck path

Mp00100
Dyck paths ⟶ Integer compositions

touch composition

Mp00102
Dyck paths ⟶ Integer compositions

rise composition

swap returns and last-descent

to 321-avoiding permutation (Krattenthaler)

Lalanne-Kreweras involution

Cori-Le Borgne involution

Elizalde-Deutsch bijection

Barnabei-Castronuovo involution

Adin-Bagno-Roichman transformation

left-to-right-maxima to Dyck path

to 321-avoiding permutation (Billey-Jockusch-Stanley)

switch returns and last double rise

Mp00137
Dyck paths ⟶ Alternating sign matrices

to symmetric ASM

Mp00138
Dyck paths ⟶ Set partitions

to noncrossing partition

logarithmic height to pruning number

pruning number to logarithmic height

Mp00146
Dyck paths ⟶ Perfect matchings

to noncrossing matching