Séminaire Lotharingien de Combinatoire, 82B.30 (2019), 12 pp.
Hyunsoo Cho, JiSun Huh, and Jaebum Sohn
A bijection between ordinary partitions and self-conjugate partitions with same disparity
Abstract.
We give a bijection between the set of ordinary partitions and that of self-conjugate partitions with some restrictions. Also, we show the relation between hook lengths of self conjugate partition and corresponding partition via the bijection. As a corollary, we give new combinatorial interpretations for the Catalan number and the Motzkin number in terms of self-conjugate simultaneous core partitions.
Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.
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