6 papers · 1 filter
Proof of Almkvist's conjecture on the unimodality of partition polynomials
Jianxi Mao, Wenle Shi, Bao-xuan Zhu
For integers and , let The coefficient of in \(F_{r,n}(q)\) counts partitions of into parts at most…
Hankel determinants of Catalan-like sequences
Shane Chern, Wenle Shi
In this paper, we compute the (shifted) Hankel determinants of Catalan-like sequences, which arise naturally from the weighted enumerations of nonintersecting Motzkin meanders. Amo…
The analytic properties of Hoggatt triangles
Jianxi Mao, Wenle Shi
The -Hoggatt triangle is a lower triangular matrix whose entries are given by specific minors of Pascal's triangle formed by consecutive rows and columns. The cases $d=1…
Proof of Cigler's conjecture on -Hoggatt numbers
Shane Chern, Wenle Shi
We prove the nonnegativity and palindromicity of a family of polynomials arising from -Hoggatt numbers. The nonnegativity is derived from Stanley's -partition theory thro…
Some statistics on generalized Motzkin paths with vertical steps
Yidong Sun, Di Zhao, Wenle Shi +1
Recently, several authors have considered lattice paths with various steps, including vertical steps permitted. In this paper, we consider a kind of generalized Motzkin paths, call…
Symmetric and asymmetric peaks or valleys in (partial) Dyck paths
Yidong Sun, Wenle Shi, Di Zhao
The concepts of symmetric and asymmetric peaks in Dyck paths were introduced by Flórez and Ram\'ırez, who counted the total number of such peaks over all Dyck paths of a given leng…