8 papers · 1 filter
Strong -log-convexity of the -Hoggatt polynomials
Shane Chern, Wenle Shi
In this paper, three (-)log-convexity or concavity properties related to the -Hoggatt numbers are investigated. First, we show that the -Hoggatt transformation preserves t…
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…
Convolutive sequences, II: Parametrizations
Shane Chern, Dennis Eichhorn, Shishuo Fu +1
In recent work, the authors defined a sequence to be -convolutive exactly if \begin{align*} \sum_{n\ge 0} a_{mn} q^n = \left(\sum_{n\ge 0} a_n q^n\right)^m \end…
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…
Finite Kleshchev bipartitions and -trinomial coefficients
Shane Chern
The Kleshchev multipartitions arise in the representation theory for the Ariki-Koike algebras. In previous work, Li, Stanton, Xue, Yee, and the author considered a refined enumerat…
On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories
Shane Chern, Chanh Tran, Tanay Wakhare
We prove a fermionic-bosonic duality relation for the Macdonald index in Argyres-Douglas theories of type , thereby yielding a conjectural fermionic formula due to…
Signed counting of partition matrices
Shane Chern, Shishuo Fu
We prove that the signed counting (with respect to the parity of the ``'' statistic) of partition matrices equals the cardinality of a subclass of inversion seq…
Convolutive sequences, I: Through the lens of integer partition functions
Shane Chern, Dennis Eichhorn, Shishuo Fu +1
Motivated by the convolutive behavior of the counting function for partitions with designated summands in which all parts are odd, we consider coefficient sequences $(a_n)_{n\ge 0}…