论文标题
关于施密特问题及其变体的有限类似物
On Finite Analogs of Schmidt's Problem and Its Variants
论文作者
论文摘要
我们完善了Schmidt的问题和与2色分区相关的分区身份，我们将其称为Uncu-Andrews-Paule定理。我们将使用berkovich-Warnaar的Rogers-Szegő多项式上的Boulet-Stanley重量和一个公式解决问题，并提出各种Schmidt的问题定理及其改进。我们的新施密特类型结果包括使用均匀索引的零件的总和，交替的零件和钩长度以及奇数索引的零件总和，这些零件的总和出现在原始Schmidt的问题中。我们还将Schmidt的一些问题关系转化为与Rogers-Ramanujan分区有关的加权分区计数。
We refine Schmidt's problem and a partition identity related to 2-color partitions which we will refer to as Uncu-Andrews-Paule theorem. We will approach the problem using Boulet-Stanley weights and a formula on Rogers-Szegő polynomials by Berkovich-Warnaar, and present various Schmidt's problem alike theorems and their refinements. Our new Schmidt type results include the use of even-indexed parts' sums, alternating sum of parts, and hook lengths as well as the odd-indexed parts' sum which appears in the original Schmidt's problem. We also translate some of our Schmidt's problem alike relations to weighted partition counts with multiplicative weights in relation to Rogers-Ramanujan partitions.
