AbstractIt is known that the area of all Catalan paths of length n is equal to 4n−2n+1n, which coincides with the number of inversions of all 321-avoiding permutations of length n+1. In this paper, a bijection between the two sets is established. Meanwhile, a number of interesting bijective results that pave the way to the required bijection are presented
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...
AbstractMany interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible...
AbstractIt is known that the area of all Catalan paths of length n is equal to 4n−2n+1n, which coinc...
AbstractA Catalan path of length n, is a path from (0,0) going N=(0,1) or E=(0,1) in each step, such...
AbstractThis paper deals with a study of the class P of lattice paths, made of north, east, south, a...
Dyck paths having height at most $h$ and without valleys at height $h-1$ are combinatorially interpr...
AbstractThe number of even 321-avoiding permutations of length n is equal to the number of odd ones ...
AbstractCatalan numbers C(n)=1/(n+1)2nn enumerate binary trees and Dyck paths. The distribution of p...
AbstractThis paper investigates determining the statistics satisfying the Narayana distribution on t...
AbstractMany interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible...
AbstractA Catalan path of length n, is a path from (0,0) going N=(0,1) or E=(0,1) in each step, such...
AbstractThe Fine numbers and the Catalan numbers are intimately related. Two manifestations are the ...
A simple bijection is established between Morgan trees and Dyck paths. As a consequence, exact enume...
AbstractA permutation π ϵ Sn avoids the subpattern τ iff π has no subsequence having all the same pa...
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...
AbstractMany interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible...
AbstractIt is known that the area of all Catalan paths of length n is equal to 4n−2n+1n, which coinc...
AbstractA Catalan path of length n, is a path from (0,0) going N=(0,1) or E=(0,1) in each step, such...
AbstractThis paper deals with a study of the class P of lattice paths, made of north, east, south, a...
Dyck paths having height at most $h$ and without valleys at height $h-1$ are combinatorially interpr...
AbstractThe number of even 321-avoiding permutations of length n is equal to the number of odd ones ...
AbstractCatalan numbers C(n)=1/(n+1)2nn enumerate binary trees and Dyck paths. The distribution of p...
AbstractThis paper investigates determining the statistics satisfying the Narayana distribution on t...
AbstractMany interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible...
AbstractA Catalan path of length n, is a path from (0,0) going N=(0,1) or E=(0,1) in each step, such...
AbstractThe Fine numbers and the Catalan numbers are intimately related. Two manifestations are the ...
A simple bijection is established between Morgan trees and Dyck paths. As a consequence, exact enume...
AbstractA permutation π ϵ Sn avoids the subpattern τ iff π has no subsequence having all the same pa...
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...
AbstractMany interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible...
DOI
Add to ORKG