Let NT(r,k,n) count the total number of parts among partitions of n with rank congruent to r modulo k and let Mω(r,k,n) count the total appearances of ones among partitions of n with crank congruent to r modulo k. We provide a list of over 70 congruences modulo 5, 7, 11 and 13 involving NT(r,k,n) and Mω(r,k,n), which are known as congruences of Andrews–Beck type. Some recent conjectures of Chan, Mao and Osburn are also included in this list.

中文翻译：

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加权分区秩和曲柄矩。三、Andrews-Beck 类型同余模 5、7、11 和 13 的列表

让ñ吨(r,ķ,n)计算分区之间的零件总数n与等级一致r模数ķ然后让米ω(r,ķ,n)计算分区中的总出现次数n与曲柄一致r模数ķ. 我们提供了 70 多个同余模的列表5,7,11和13涉及ñ吨(r,ķ,n)和米ω(r,ķ,n), 称为 Andrews-Beck 类型的同余。Chan、Mao 和 Osburn 最近的一些猜想也包括在这个列表中。