17 citations · 47 across the 25 of their papers we have counts for
7 papers · 1 filter
Several -series related to Ramanujan's theta functions
Dazhao Tang, Ernest. X. W. Xia
Quite recently, the first author investigated vanishing coefficients of the arithmetic progressions in several -series expansions. In this paper, we further study the signs of c…
Elementary proof of congruences modulo 25 for broken -diamond partitions
Shane Chern, Dazhao Tang
Let denote the number of -broken diamond partitions of . Quite recently, the second author proved an infinite family of congruences modulo 25 for with t…
Congruences modulo powers of 3 for 2-color partition triples
Dazhao Tang
Let enumerate the number of 2-color partition triples of where one of the colors appears only in parts that are multiples of . In this paper, we prove several i…
Some inequalities for Garvan's bicrank function of 2-colored partitions
Shane Chern, Dazhao Tang, Liuquan Wang
In order to provide a unified combinatorial interpretation of congruences modulo for 2-colored partition functions, Garvan introduced a bicrank statistic in terms of weighted v…
-Catalan numbers: gamma expansions, pattern avoidance and the -phenomenon
Shishuo Fu, Dazhao Tang, Bin Han +1
The aim of this paper is two-fold. We first prove several new interpretations of a kind of -Catalan numbers along with their corresponding -expansions using pattern avoid…
Multi-dimensional -summations and multi-colored partitions
Shane Chern, Shishuo Fu, Dazhao Tang
Motivated by Alladi's recent multi-dimensional generalization of Sylvester's classical identity, we provide a simple combinatorial proof of an overpartition analogue, which contain…
On certain unimodal sequences and strict partitions
Shishuo Fu, Dazhao Tang
Building on a bijection of Vandervelde, we enumerate certain unimodal sequences whose alternating sum equals zero. This enables us to refine the enumeration of strict partitions wi…