Séminaire Lotharingien de Combinatoire, 89B.39 (2023), 12 pp.
Cristina Ballantine, Hannah Burson, William Craig,
Amanda Folsom and Boya Wen
Hook Length Bias in Odd versus Distinct Partitions
Abstract.
Motivated in part by hook-content formulas for certain restricted partitions in representation theory, we consider the total number of hooks of fixed length in odd versus distinct partitions. We show that there are more hooks of length 2, respectively 3, in all odd partitions of n than in all distinct partitions of n, and make the analogous conjecture for arbitrary hook length t ≥ 2. To this end, we establish very general linear inequalities for the number of distinct partitions, which is also of independent interest. We also establish additional related partition bias results.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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