10 citations · 11 across the 11 of their papers we have counts for
15 papers · 1 filter
Burstein's permutation conjecture, Hong and Li's inversion sequence conjecture, and restricted Eulerian distributions
Shane Chern, Shishuo Fu, Zhicong Lin
Recently, Hong and Li launched a systematic study of length-four pattern avoidance in inversion sequences, and in particular, they conjectured that the number of -avoiding in…
Linked partition ideals and the Alladi--Schur theorem
George E. Andrews, Shane Chern, Zhitai Li
Let denote the set of integer partitions into parts that differ by at least , with the added constraint that no two consecutive multiples of occur as parts. We…
Reciprocity between partitions and compositions
George Beck, Shane Chern
In this paper, we extend the work of Andrews, Beck and Hopkins by considering partitions and compositions with bounded gaps between each pair of consecutive parts. We show that bot…
On 0012-avoiding inversion sequences and a Conjecture of Lin and Ma
Shane Chern
The study of pattern avoidance in inversion sequences recently attracts extensive research interests. In particular, Zhicong Lin and Jun Ma conjectured a formula that counts the nu…
Vanishing coefficients in several -series expansions related to the Rogers--Ramanujan continued fraction
Shane Chern, Dazhao Tang
In this paper, we investigate several infinite products with vanishing Taylor coefficients in arihmetic progressions. These infinite products are closely related to the Rogers--Ram…
5-Dissections and sign patterns of Ramanujan's parameter and its companion
Shane Chern, Dazhao Tang
In 1998, Michael Hirschhorn discovered 5-dissections of the Rogers--Ramanujan continued fraction and its reciprocal. In this paper, we obtain the 5-dissections for functions…