Armstrong's Conjecture for $(k,mk+1)$-Core Partitions

Abstract

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 $b-1$.

17 pages, 3 figures

Cited by in corpus (2)

• Symmetry in maximal $(s-1,s+1)$ cores
• On self-conjugate $(s,s+1,\dots ,s+k)$-core partitions