论文标题
$ k，l $ regarbular分区的算术组合
The arithmetical combinatorics of $k,l$-regular partitions
论文作者
论文摘要
对于所有正整数$ k，l，n $，Little Glaisher定理指出，$ n $ $ n $的分区数量不可除以$ k $，并且发生少于$ l $ times等于$ n $ $ n $的零件数量，而不是$ l $不划分的零件，并且发生的零件量低于$ k $ times。虽然通过计算生成函数来易于确定Glaisher定理的这种完善，但仍然没有一对一的规范通信来解释它。我们的论文通过算术方法为这个开放问题带来了答案。此外，在$ l = 2 $的情况下，我们讨论了通过加权词构建小魅力定理的Schur型伴侣的可能性。
For all positive integers $k,l,n$, the Little Glaisher theorem states that the number of partitions of $n$ into parts not divisible by $k$ and occurring less than $l$ times is equal to the number of partitions of $n$ into parts not divisible by $l$ and occurring less than $k$ times. While this refinement of Glaisher theorem is easy to establish by computation of the generating function, there is still no one-to-one canonical correspondence explaining it. Our paper brings an answer to this open problem through an arithmetical approach. Furthermore, in the case $l=2$, we discuss the possibility of constructing a Schur-type companion of the Little Glaisher theorem via the weighted words.
