A Chinese Remainder Theorem for Partitions
@inproceedings{Seethalakshmi2021ACR,
title={A Chinese Remainder Theorem for Partitions},
author={K. A. Seethalakshmi and Steven Spallone},
year={2021}
}Let s, t be natural numbers, and fix an s-core partition σ and a t-core partition τ . Put d = gcd(s, t) and m = lcm(s, t), and write Nσ,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, Nσ,τ (k) is a quasipolynomial of period m and degree 1 d (s− d)(t− d).
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