7 papers
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…
Tadpole Nahm sum as a Wronskian
Shane Chern, Chanh Tran, Tanay Wakhare
We show that the tadpole Nahm sum is essentially a specialization of a series studied by Bartlett and Warnaar. This overlooked connection was first discovered by the internal model…
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 thr…
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…