7 papers · 1 filter
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…
On mesh patterns of short length: Equidistribution and enumeration
Qi Fang, Shishuo Fu, Sergey Kitaev +3
The classification and enumeration of short mesh patterns have emerged as two central directions in the area. We make substantial progress on both fronts. We construct an involutio…
An involution for trivariate symmetries of vincular patterns
Joanna N. Chen, Shishuo Fu, Jiang Zeng
We provide a bijective proof of the equidistribution of two pairs of vincular patterns in permutations, thereby resolving a recent open problem of Bitonti, Deb, and Sokal (arXiv:24…
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}…
A refined view of a curious identity for partitions into odd parts with designated summands
Shishuo Fu, James Sellers
In 2002, Andrews, Lewis, and Lovejoy introduced the combinatorial objects which they called partitions with designated summands. These are constructed by taking unrestricted intege…