论文标题
整数分区的组合和规定的周长
Combinatorics of Integer Partitions With Prescribed Perimeter
论文作者
论文摘要
我们证明，重复零件的偶数数量和零件的次数在用固定周长的整数分区上具有相同的分布。这可以完善Straub对Euler奇怪的分区定理的类似物。我们将两个相关统计数据概括到零件差异的少于$ d $的情况下，这些零件不一致，不一致$ 1 $ modulo $ d+1 $，并证明了分配不平等，其风味与alder的前注射相似，而不是与规定的外观分区。我们的两个结果均在分析和组合上得到证明。
We prove that the number of even parts and the number of times that parts are repeated have the same distribution over integer partitions with a fixed perimeter. This refines Straub's analog of Euler's Odd-Distinct partition theorem. We generalize the two concerned statistics to these of the part-difference less than $d$ and the parts not congruent to $1$ modulo $d+1$ and prove a distribution inequality, that has a similar flavor as Alder's ex-conjecture, over partitions with a prescribed perimeter. Both of our results are proved analytically and combinatorially.
