4 papers
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…