论文标题
Schmidt-Type定理的指行业方法
Bijective Approaches for Schmidt-Type Theorems
论文作者
论文摘要
我们通过研究两种射击提供了新的施密特型结果，这是涉及仅在给定指数计数的零件的分区的结果。莫克（Mork）的两者是第一个，最初是作为施密特定理的证明。我们表明，Sylvester的两次射击版本等效于Mork的两种模块图，这意味着现有结果的改进和新的生成功能身份。然后，我们根据在Andrews and Keith的最新论文中出现的想法开发了两者，该想法将分区计数为$ r $，$ t+r $，$ 2T+r，$ r，\ dots $与$ t $颜色的分区相应。这导致了对桥梁和UNCU身份的实质性概括，并对Li和Yee进行了类似的研究。
We provide new Schmidt-type results through an investigation of two bijections, which are results involving partitions with parts counted only at given indices. Mork's bijection, the first of these, was originally given as a proof of Schmidt's theorem. We show that a version of Sylvester's bijection is equivalent to Mork's bijection applied to 2-modular diagrams, which implies refinements of existing results and new generating function identities. We then develop a bijection based on an idea appearing in a recent paper of Andrews and Keith, that places partitions counted at the indices $r$, $t+r$, $2t+r, \dots$ in correspondence with $t$-colored partitions. This leads to a substantial generalization of an identity of Bridges and Uncu, and complements a similar investigation of Li and Yee.
