Helen W. J. Zhang

activity

20182023

most citedThe Unimodality of the Crank on Overpartitions

3 citations · 3 across the 8 of their papers we have counts for

collaborators

10 papers

math.NT2023

Inequalities for the $k$ -Regular Overpartitions

Yi Peng, Helen W. J. Zhang, Ying Zhong

Bessenrodt and Ono, Chen, Wang and Jia, DeSalvo and Pak were the first to discover the log-subadditivity, log-concavity, and the third-order Turán inequality of partition function,…

math.CO2023

Asymptotics for $k$ -crank of $k$ -colored partitions

Helen W. J. Zhang, Ying Zhong

In this paper, we obtain asymptotic formulas for $k$ -crank of $k$ -colored partitions. Let $M_{k} (a, c; n)$ denote the number of $k$ -colored partitions of $n$ with a $k$ -crank congrue…

math.NT2022

Congruences for modular forms and applications to crank functions

Hao Zhang, Helen W. J. Zhang

In this paper, motivated by the work of Mahlburg, we find congruences for a large class of modular forms. Moreover, we generalize the generating function of the Andrews-Garvan-Dyso…

math.CO2022

Strict Log-Subadditivity for Overpartition Rank

Helen W. J. Zhang, Ying Zhong

Bessenrodt and Ono initially found the strict log-subadditivity of partition function $p (n)$ , that is, $p (a + b) < p (a) p (b)$ for $a, b > 1$ and $a + b > 9$ . Many other important statistics o…

math.CO2022

Asymptotic formula for the $M_{2}$ -ranks of overpartitions

Helen W. J. Zhang, Ying Zhong

Let $N_{2} (a, c, n)$ be the number of overpartitions of $n$ whose the $M_{2}$ -rank is congruent to $a$ modulo $c$ . In this paper, we obtain the asymptotic formula of $\overlin…

math.NT2022

Higher order log-concavity of the overpartition function and its consequences

Gargi Mukherjee, Helen W. J. Zhang, Ying Zhong

Let $p ˉ (n)$ denote the overpartition function. In this paper, we study the asymptotic higher order $lo g$ -concavity property of the overpatition function in a similar framewor…

math.CO2018★ 3 cited

The Unimodality of the Crank on Overpartitions

Wenston J. T. Zang, Helen W. J. Zhang

Let $N (m, n)$ denote the number of partitions of $n$ with rank $m$ , and let $M (m, n)$ denote the number of partitions of $n$ with crank $m$ . Chan and Mao proved that for any nonnegat…

math.CO2018

Inequalities for the overpartition function

Edward Y. S. Liu, Helen W. J. Zhang

Let $p (n)$ denote the overpartition funtion. Engel showed that for $n \geq 2$ , $p (n)$ satisfied the Turán inequalities, that is, $\overline{p}(n)^2-\overline{p}…

math.CO2018

$M_{2}$ -Ranks of overpartitions modulo $6$ and $10$

Helen W. J. Zhang

In this paper, we obtain inequalities on $M_{2}$ -ranks of overpartitions modulo $6$ . Let $N_{2} (s, m, n)$ to be the number of overpartitions of $n$ whose $M_{2}$ -rank is congrue…

math.CO2018

Generalized Lambert Series Identities and Applications in Rank Differences

Bin Wei, Helen W. J. Zhang

In this article, we prove two identities of generalized Lambert series. By introducing what we call $S$ -series, we establish relationships between multiple generalized La…

Inequalities for the k-Regular Overpartitions

Asymptotics for k-crank of k-colored partitions

Congruences for modular forms and applications to crank functions

Strict Log-Subadditivity for Overpartition Rank

Asymptotic formula for the M2​-ranks of overpartitions

Higher order log-concavity of the overpartition function and its consequences

The Unimodality of the Crank on Overpartitions

Inequalities for the overpartition function

M2​-Ranks of overpartitions modulo 6 and 10

Generalized Lambert Series Identities and Applications in Rank Differences

Inequalities for the $k$ -Regular Overpartitions

Asymptotics for $k$ -crank of $k$ -colored partitions

Asymptotic formula for the $M_{2}$ -ranks of overpartitions

$M_{2}$ -Ranks of overpartitions modulo $6$ and $10$