Self-conjugate partitions with the same disparity

Hyunsoo Cho; Ji Sun Huh; Jaebum Sohn

doi:10.1016/j.disc.2019.111806

Self-conjugate partitions with the same disparity

Hyunsoo Cho, Ji Sun Huh, Jaebum Sohn

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We give a bijection between the set of ordinary partitions and that of self-conjugate partitions with some restrictions. Also, we show the relationship between hook lengths of a self-conjugate partition and its 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.

Original language	English
Article number	111806
Journal	Discrete Mathematics
Volume	343
Issue number	5
DOIs	https://doi.org/10.1016/j.disc.2019.111806
Publication status	Published - 2020 May

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2019.111806

Cite this

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AB - We give a bijection between the set of ordinary partitions and that of self-conjugate partitions with some restrictions. Also, we show the relationship between hook lengths of a self-conjugate partition and its 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.

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Self-conjugate partitions with the same disparity

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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