Dazhao Tang

activity

20162026

most citedGeneralizing a partition theorem of Andrews

17 citations · 47 across the 25 of their papers we have counts for

collaborators

25 papers

math.NT2026

An elementary approach to Sun Kim's general theta function identities

Dazhao Tang

Ramanujan's modular equations of degrees $3$ , $5$ , $7$ , $11$ and $23$ are closely related to certain theta function identities. Warnaar generalized the identities arising from the…

math.NT2026

On the occurrence of congruence multiplicities between Ramanujan's theta functions

Shane Chern, Nicolas Allen Smoot, Dazhao Tang

Recently, the first and third authors initiated a study of arithmetical relationships between Ramanujan's theta functions $φ (- q)$ and $ψ (q)$ . In this work, we prove eight families…

math.NT2026

Identities and transformations for Lambert series and double Lambert series

Su-Ping Cui, Dazhao Tang

We establish two identities for Lambert series and double Lambert series, thereby resolving conjectures of Andrews, Dixit, Schultz and Yee (Acta Arith.~181:253--286, 2017), as well…

math.NT2023

Ramanujan's theta functions and internal congruences modulo arbitrary powers of $3$

Shane Chern, Dazhao Tang

In this work, we investigate internal congruences modulo arbitrary powers of $3$ for two functions arising from Ramanujan's classical theta functions $φ (q)$ and $ψ (q)$ . By letting…

math.NT2023★ 6 cited

Partitions with parts separated by parity: conjugation, congruences and the mock theta functions

Shishuo Fu, Dazhao Tang

Noting a curious link between Andrews' even-odd crank and the Stanley rank, we adopt a combinatorial approach building on the map of conjugation and continue the study of integer p…

math.NT2022★ 2 cited

General coefficient-vanishing results associated with theta series

Shane Chern, Dazhao Tang

There are a number of sporadic coefficient-vanishing results associated with theta series, which suggest certain underlying patterns. By expanding theta powers as linear combinatio…

math.NT2022

A conjecture of Baruah and Begum on the smallest parts function of restricted overpartitions

Dazhao Tang

In 2017, Andrews, Dixit, Schultz and Yee introduced the function $spt_{ω} (n)$ , which denotes the number of smallest parts in the overpartitions of $n$ in which th…

math.CO2020

Vanishing coefficients in several $q$ -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…

math.CO2020

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 $R (q)$ and its reciprocal. In this paper, we obtain the 5-dissections for functions…

math.CO2019

Vanishing coefficients in some $q$ -series expansions

Dazhao Tang

Motivated by the recent work of Hirschhorn on vanishing coefficients of the arithmetic progressions in certain $q$ -series expansions, we study some variants of these $q$ -series and…

math.CO2019★ 1 cited

A lecture hall theorem for $m$ -falling partitions

Shishuo Fu, Dazhao Tang, Ae Ja Yee

For an integer $m \geq 2$ , a partition $λ = (λ_{1}, λ_{2}, \dots)$ is called $m$ -falling, a notion introduced by Keith, if the least nonnegative residues mod $m$ of $λ_{i}$ 's form a nonincrea…

math.CO2018★ 1 cited

Several $q$ -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 $q$ -series expansions. In this paper, we further study the signs of c…

math.CO2018★ 3 cited

Elementary proof of congruences modulo 25 for broken $k$ -diamond partitions

Shane Chern, Dazhao Tang

Let $Δ_{k} (n)$ denote the number of $k$ -broken diamond partitions of $n$ . Quite recently, the second author proved an infinite family of congruences modulo 25 for $Δ_{k} (n)$ with t…

math.CO2018

Congruences modulo powers of 3 for 2-color partition triples

Dazhao Tang

Let $p_{k, 3} (n)$ enumerate the number of 2-color partition triples of $n$ where one of the colors appears only in parts that are multiples of $k$ . In this paper, we prove several i…

math.CO2018

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 $5$ for 2-colored partition functions, Garvan introduced a bicrank statistic in terms of weighted v…

math.CO2018★ 1 cited

$(q, t)$ -Catalan numbers: gamma expansions, pattern avoidance and the $(- 1)$ -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 $(q, t)$ -Catalan numbers along with their corresponding $γ$ -expansions using pattern avoid…

math.CO2018

Multi-dimensional $q$ -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…

math.CO2018

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…

math.CO2017

Congruences modulo powers of 5 for $k$ -colored partitions

Dazhao Tang

Let $p_{- k} (n)$ enumerate the number of $k$ -colored partitions of $n$ . In this paper, we establish some infinite families of congruences modulo 25 for $k$ -colored partitions. Furth…

math.CO2017

New congruences for broken $k$ -diamond partitions

Dazhao Tang

The notion of broken $k$ -diamond partitions was introduced by Andrews and Paule. Let $Δ_{k} (n)$ denote the number of broken $k$ -diamond partitions of $n$ for a fixed positive integ…

math.CO2017★ 1 cited

On a generalized crank for $k$ -colored partitions

Shishuo Fu, Dazhao Tang

A generalized crank ( $k$ -crank) for $k$ -colored partitions is introduced. Following the work of Andrews-Lewis and Ji-Zhao, we derive two results for this newly defined $k$ -crank. N…

math.CO2017

On certain weighted 7-colored partitions

Shane Chern, Dazhao Tang

Inspired by Andrews' 2-colored generalized Frobenius partitions, we consider certain weighted 7-colored partition functions and establish some interesting Ramanujan-type identities…

math.CO2017★ 17 cited

Generalizing a partition theorem of Andrews

Shishuo Fu, Dazhao Tang

Motivated by Andrews' recent work related to Euler's partition theorem, we consider the set of partitions of an integer $n$ where the set of even parts has exactly $j$ elements, ve…

math.CO2016★ 15 cited

Multiranks and classical theta functions

Shishuo Fu, Dazhao Tang

Multiranks and new rank/crank analogs for a variety of partitions are given, so as to imply combinatorially some arithmetic properties enjoyed by these types of partitions. Our met…

An elementary approach to Sun Kim's general theta function identities

On the occurrence of congruence multiplicities between Ramanujan's theta functions

Identities and transformations for Lambert series and double Lambert series

Ramanujan's theta functions and internal congruences modulo arbitrary powers of 3

Partitions with parts separated by parity: conjugation, congruences and the mock theta functions

General coefficient-vanishing results associated with theta series

A conjecture of Baruah and Begum on the smallest parts function of restricted overpartitions

Vanishing coefficients in several q-series expansions related to the Rogers--Ramanujan continued fraction

5-Dissections and sign patterns of Ramanujan's parameter and its companion

Vanishing coefficients in some q-series expansions

A lecture hall theorem for m-falling partitions

Several q-series related to Ramanujan's theta functions

Elementary proof of congruences modulo 25 for broken k-diamond partitions

Congruences modulo powers of 3 for 2-color partition triples

Some inequalities for Garvan's bicrank function of 2-colored partitions

(q,t)-Catalan numbers: gamma expansions, pattern avoidance and the (−1)-phenomenon

Multi-dimensional q-summations and multi-colored partitions

On certain unimodal sequences and strict partitions

Congruences modulo powers of 5 for k-colored partitions

New congruences for broken k-diamond partitions

On a generalized crank for k-colored partitions

On certain weighted 7-colored partitions

Generalizing a partition theorem of Andrews

Multiranks and classical theta functions

Ramanujan's theta functions and internal congruences modulo arbitrary powers of $3$

Vanishing coefficients in several $q$ -series expansions related to the Rogers--Ramanujan continued fraction

Vanishing coefficients in some $q$ -series expansions

A lecture hall theorem for $m$ -falling partitions

Several $q$ -series related to Ramanujan's theta functions

Elementary proof of congruences modulo 25 for broken $k$ -diamond partitions

$(q, t)$ -Catalan numbers: gamma expansions, pattern avoidance and the $(- 1)$ -phenomenon

Multi-dimensional $q$ -summations and multi-colored partitions

Congruences modulo powers of 5 for $k$ -colored partitions

New congruences for broken $k$ -diamond partitions

On a generalized crank for $k$ -colored partitions