Armstrong's conjecture for (k, mk+1)-core partitions

作者：Aggarwal Amol^*

来源：European Journal of Combinatorics, 2015, 47: 54-67.

DOI：10.1016/j.ejc.2015.01.008

A conjecture of Armstrong states that if gcd(a,b)=1 , then the average size of an (a,b) -core partition is (a-1)(b-1)(a+b+1)/24 . Recently, Stanley and Zanello used a recursive argument to verify this conjecture when a=b-1 . In this paper we use a variant of their method to establish Armstrong's conjecture in the more general setting where a divides b-1.

• 出版日期2015-7
• 单位MIT