A Chinese Remainder Theorem for Partitions

Abstract

Given natural numbers s, t such that gcd(s, t) = d, lcm(s, t) = m, an s-core σ, and a t-core τ , we write N_{σ, τ}(k) for the number of m-cores of length no greater than k whose s-core is σ and t-core is τ. In this thesis, we prove that, for k >> 0, N_{σ, τ}(k) is a quasi-polynomial of quasi-period m and degree (s-d)(t-d)/d.