论文标题
在$ k $ - measure和durfee式隔板方面
On $k$-measures and Durfee squares of partitions
论文作者
论文摘要
最近，安德鲁斯（Andrews），巴塔赫吉（Bhattacharjee）和达斯蒂达（Dastidar）介绍了$ k $的概念 - 整数分区的概念，并证明令人惊讶的是，具有$ 2 $ n $的分区的数量，$ 2 $ 2 $ measure $ m $等于$ n $ a $ n $ a durfee side side $ m $ $ m $ $ m $。作者要求提供该结果的徒证明，并提出进一步探索$ n $的分区数量的属性，这些分区数量为$ k $ - measure $ m $ for $ k \ geq 3 $。在本说明中，我们完成了这些任务。也就是说，我们获得了Andrews，Bhattacharjee和Dastidar的结果的简短组合证明，并且使用此证明，我们可以轻松地将此结果推广到$ k $ - 量子。
Recently, Andrews, Bhattacharjee and Dastidar introduced the concept of $k$-measure of an integer partition, and proved a surprising identity that the number of partitions of $n$ which have $2$-measure $m$ is equal to the number of partitions of $n$ with a Durfee square of side $m$. The authors asked for a bijective proof of this result and also suggested a further exploration of the properties of the number of partitions of $n$ which have $k$-measure $m$ for $k \geq 3$. In this note, we complete these tasks. That is, we obtain a short combinatorial proof of the result of Andrews, Bhattacharjee and Dastidar, and using this proof, we easily generalize this result for $k$-measures.
