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
AbstractMany interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible...
AbstractWe develop an arithmetic triangle similar to Pascal's triangle. The entries are interpreted ...
AbstractA new identity is obtained for the Catalan triangle introduced by Shapiro
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...
AbstractThe sum of the areas of (2n+2)-length Dyck paths, or total area, is equal to the number of p...
AbstractIf α = {α0, α1,…, αn} and β = {β0, β1,…, βn} are two non-decreasing sets of integers such th...
AbstractA lattice path is a path on lattice points (points with integer coordinates) in the plane in...
AbstractThe sum of the areas of (2n+2)-length Dyck paths, or total area, is equal to the number of p...
AbstractFor fixed positive integer k, let En denote the set of lattice paths using the steps (1,1), ...
AbstractWe deal with non-decreasing paths on the non-negative quadrant of the integral square lattic...
Many interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible general...
Colloque avec actes et comité de lecture. internationale.International audienceWe present a method, ...
This paper is about the Catalan numbers. The paper is organized as fol-lows: section 1 presents a wi...
AbstractMany interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible...
AbstractWe develop an arithmetic triangle similar to Pascal's triangle. The entries are interpreted ...
AbstractA new identity is obtained for the Catalan triangle introduced by Shapiro
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...
AbstractThe sum of the areas of (2n+2)-length Dyck paths, or total area, is equal to the number of p...
AbstractIf α = {α0, α1,…, αn} and β = {β0, β1,…, βn} are two non-decreasing sets of integers such th...
AbstractA lattice path is a path on lattice points (points with integer coordinates) in the plane in...
AbstractThe sum of the areas of (2n+2)-length Dyck paths, or total area, is equal to the number of p...
AbstractFor fixed positive integer k, let En denote the set of lattice paths using the steps (1,1), ...
AbstractWe deal with non-decreasing paths on the non-negative quadrant of the integral square lattic...
Many interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible general...
Colloque avec actes et comité de lecture. internationale.International audienceWe present a method, ...
This paper is about the Catalan numbers. The paper is organized as fol-lows: section 1 presents a wi...
AbstractMany interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible...
AbstractWe develop an arithmetic triangle similar to Pascal's triangle. The entries are interpreted ...
AbstractA new identity is obtained for the Catalan triangle introduced by Shapiro
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