A Chinese Remainder Theorem for Partitions [article]

K. Seethalakshmi, Steven Spallone
2022 arXiv   pre-print
Let s,t be natural numbers, and fix an s-core partition σ and a t-core partition τ. Put d=(s,t) and m= lcm(s,t), and write N_σ, τ(k) for the number of m-core partitions of length no greater than k whose s-core is σ and t-core is τ. We prove that for k large, N_σ, τ(k) is a quasipolynomial of period m and degree 1/d(s-d)(t-d).
arXiv:2105.07611v2 fatcat:kcdkntvdufhudlbcmkkdsdvrzy