A PROOF OF ANDREWS’ CONJECTURE ON PARTITIONS WITH NO SHORT SEQUENCES
DANIEL M. KANE, ROBERT C. RHOADES
Forum of Mathematics, Sigma · 2019
doi:10.1017/fms.2019.8 (opens in a new tab)
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Abstract
Our main result establishes Andrews’ conjecture for the asymptotic of the generating function for the number of integer partitions of $n$ without $k$ consecutive parts. The methods we develop are applicable in obtaining asymptotics for stochastic processes that avoid patterns; as a result they yield asymptotics for the number of partitions that avoid patterns.
Abstract licence: CC BY-ND
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