论文标题
计算k在所有零件的多重性小于k的零件中可排除的零件
Counting the parts divisible by k in all the partitions of n whose parts have multiplicity less than k
论文作者
论文摘要
Andrews and Merca的最新结果是通过生成函数得出的，n分区中的所有分区中的均匀部分数量是A（n）。本文将这些结果扩展到k在所有n个分区中可除以K的零件数，而n的所有分区都严格少于k，ak（n）。此外，使用Glaisher的两者进行的扩展提供了组合证明。最后，我们给出了这个新的整数序列家族的生成功能，并使用它来验证广义五边形，三角形和平方功率复发关系。
Recent results by Andrews and Merca on the number of even parts in all partitions of n into distinct parts, a(n), were derived via generating functions. This paper extends these results to the number of parts divisible by k in all the partitions of n for which the multiplicity of each part is strictly less than k, ak(n). Moreover, a combinatorial proof is provided using an extension of Glaisher's bijection. Finally, we give the generating functions for this new family of integer sequences and use it to verify generalized pentagonal, triangular, and square power recurrence relations.
