波兰科学研究院数学研究所
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作者:Heng Huat Chan , Liuquan Wang
来源:[J].Acta Arithmetica(IF 0.472), 2019, Vol.187, pp.59-80IMPAS
摘要:Let $p_{k}(n)$ be the coefficient of $q^n$ in the series expansion of $(q;q)_{\infty}^{k}$.It is known that the partition function $p(n)$, which corresponds to the case when $k=-1$, satisfiescongruences such as $p(5n+4)\equiv 0\pmod{5}$. In this article, we discusscongruences sat...
作者:Shane Chern , Dazhao Tang , Liuquan Wang
来源:[J].Acta Arithmetica(IF 0.472), 2019, Vol.190, pp.171-191IMPAS
摘要: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 vector partitions. In this paper, we obtain some inequalities between the bicrank counts $M^{*}(...
作者:Chao Gu , Liuquan Wang , Ernest X. W. Xia
来源:[J].Acta Arithmetica(IF 0.472), 2016, Vol.175, pp.291-300IMPAS
摘要:In his 1984 AMS Memoir, Andrews introduced the $k$-colored generalized Frobenius partition function. Let $c\phi _k(n)$ denote the number of generalized Frobenius partitions of $n$ with $k$ colors. Recently, congruences modulo 4, 9 and 27 for $c\phi _6(n)$ were proved by Baruah an...

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