AbstractA Catalan path of length n, is a path from (0,0) going N=(0,1) or E=(0,1) in each step, such that it stays under (or on) the line x=y and ending at (n,n) after 2n steps. Here we calculate the total area between the line y=x and all Catalan paths. The total area an=12∑k=1nck4n−k, where ck is the number of Catalan paths of length k
AbstractCatalan numbers C(n)=1/(n+1)2nn enumerate binary trees and Dyck paths. The distribution of p...
AbstractWe consider sequences of polynomials which count lattice paths by area. In some cases the re...
AbstractGiven a sequence of integers b=(b0,b1,b2,…) one gives a Dyck path P of length 2n the weightw...
AbstractA Catalan path of length n, is a path from (0,0) going N=(0,1) or E=(0,1) in each step, such...
AbstractIt is known that the area of all Catalan paths of length n is equal to 4n−2n+1n, which coinc...
AbstractIt is known that the area of all Catalan paths of length n is equal to 4n−2n+1n, which coinc...
AbstractIf α = {α0, α1,…, αn} and β = {β0, β1,…, βn} are two non-decreasing sets of integers such th...
AbstractA new identity is obtained for the Catalan triangle introduced by Shapiro
AbstractThis paper deals with a study of the class P of lattice paths, made of north, east, south, a...
AbstractA lattice path is a path on lattice points (points with integer coordinates) in the plane in...
AbstractIf α = {α0, α1,…, αn} and β = {β0, β1,…, βn} are two non-decreasing sets of integers such th...
AbstractWe develop an arithmetic triangle similar to Pascal's triangle. The entries are interpreted ...
AbstractWe deal with non-decreasing paths on the non-negative quadrant of the integral square lattic...
AbstractThis paper investigates determining the statistics satisfying the Narayana distribution on t...
AbstractA new combinatorial interpretation is presented for generalized Catalan numbers [11], i.e., ...
AbstractCatalan numbers C(n)=1/(n+1)2nn enumerate binary trees and Dyck paths. The distribution of p...
AbstractWe consider sequences of polynomials which count lattice paths by area. In some cases the re...
AbstractGiven a sequence of integers b=(b0,b1,b2,…) one gives a Dyck path P of length 2n the weightw...
AbstractA Catalan path of length n, is a path from (0,0) going N=(0,1) or E=(0,1) in each step, such...
AbstractIt is known that the area of all Catalan paths of length n is equal to 4n−2n+1n, which coinc...
AbstractIt is known that the area of all Catalan paths of length n is equal to 4n−2n+1n, which coinc...
AbstractIf α = {α0, α1,…, αn} and β = {β0, β1,…, βn} are two non-decreasing sets of integers such th...
AbstractA new identity is obtained for the Catalan triangle introduced by Shapiro
AbstractThis paper deals with a study of the class P of lattice paths, made of north, east, south, a...
AbstractA lattice path is a path on lattice points (points with integer coordinates) in the plane in...
AbstractIf α = {α0, α1,…, αn} and β = {β0, β1,…, βn} are two non-decreasing sets of integers such th...
AbstractWe develop an arithmetic triangle similar to Pascal's triangle. The entries are interpreted ...
AbstractWe deal with non-decreasing paths on the non-negative quadrant of the integral square lattic...
AbstractThis paper investigates determining the statistics satisfying the Narayana distribution on t...
AbstractA new combinatorial interpretation is presented for generalized Catalan numbers [11], i.e., ...
AbstractCatalan numbers C(n)=1/(n+1)2nn enumerate binary trees and Dyck paths. The distribution of p...
AbstractWe consider sequences of polynomials which count lattice paths by area. In some cases the re...
AbstractGiven a sequence of integers b=(b0,b1,b2,…) one gives a Dyck path P of length 2n the weightw...
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