29 citations · 44 across the 6 of their papers we have counts for
6 papers · 1 filter
Potential Polynomials and Motzkin Paths
Yidong Sun
A {\em Motzkin path} of length is a lattice path from to in the plane integer lattice consisting of horizontal-steps , up-s…
On the number of combinations without certain separations
Toufik Mansour, Yidong Sun
In this paper we enumerate the number of ways of selecting objects from objects arrayed in a line such that no two selected ones are separated by object…
Identities involving Narayana polynomials and Catalan numbers
Toufik Mansour, Yidong Sun
We first establish the result that the Narayana polynomials can be represented as the integrals of the Legendre polynomials. Then we represent the Catalan numbers in terms of the N…
Bell Polynomials and -generalized Dyck Paths
Toufik Mansour, Yidong Sun
A {\em k-generalized Dyck path} of length is a lattice path from to in the plane integer lattice consisting of horizontal-steps $(k…
Motzkin numbers of higher rank: Generating function and explicit expression
Toufik Mansour, Matthias Schork, Yidong Sun
The generating function and an explicit expression is derived for the (colored) Motzkin numbers of higher rank introduced recently. Considering the special case of rank one yields…
Excedance numbers for permutations in complex reflection groups
Toufik Mansour, Yidong Sun
Recently, Bagno, Garber and Mansour studied a kind of excedance number on the complex reflection groups and computed its multidistribution with the number of fixed points on the se…