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

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7 papers · 1 filter

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.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.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…

Asymptotics for k-crank of k-colored partitions

Strict Log-Subadditivity for Overpartition Rank

Asymptotic formula for the M2​-ranks of overpartitions

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

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 $10$