标题： 分拆和不包含重复奇数部分的分拆的刻度的组合解释 显示英文标题

标题： Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts

摘要： 我们给出了Bringmann、Lovejoy和Osburn在2009年定义的过划分的两个剩余车轴的组合解释，类似于Andrews和第一位作者在1988年给出的划分的车轴。 作为结果，我们给出了他们定义的新版本，而无需调整权重。 此外，我们研究了无重复奇数部分的划分的$M_2$-车轴的组合解释，并探讨了这些统计量与其对应的同伴排名以及Ramanujan的第十阶拟模形式之间的联系。 显示英文摘要

摘要： We give combinatorial interpretations of two residual cranks of overpartitions defined by Bringmann, Lovejoy and Osburn in 2009 analogous to the crank of partitions given by Andrews and the first author in 1988. As a consequence, we give new versions of their definitions without adjusted weights. Furthermore, we investigate the combinatorial interpretation of an $M_2$-crank of partitions without repeated odd parts and explore connections of these statistics with their companion rank counterparts and the tenth order mock theta functions of Ramanujan.