一类限制m元over-分拆同余式

Congruences for a Restricted m-ary Overpartition Function

中文关键词:  分拆  $m$元分拆  $m$元over-分拆  生成函数.

英文关键词:partition  overpartition  $m$-ary overpartition  generating function.

中文摘要:

      本文讨论了一类限制$m$元over-分拆函数$\bar{b}_{m, j}(n)$,其中$\bar{b}_{m, j}(n)$为$n$的分拆项$m^i$至多有$i j$个的$m$元over-分拆的个数,并给出了$\bar{b}_{m, lm-1}(n)$的一族同余式.

英文摘要:

      We discuss a family of restricted $m$-ary overpartition functions $\bar{b}_{m, j}(n)$, which is the number of $m$-ary overpartitions of $n$ with at most $i j$ copies of the non-overlined part $m^i$ allowed, and obtain a family of congruences for $\bar{b}_{m, lm-1}(n)$.