A bijection between ordinary partitions and self-conjugate partitions with same disparity

Hyunsoo Cho, Jisun Huh, Jaebum Sohn

Research output: Contribution to conferencePaper

Abstract

We give a bijection between the set of ordinary partitions and that of selfconjugate 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.

Original languageEnglish
Publication statusPublished - 2019
Event31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019 - Ljubljana, Slovenia
Duration: 2019 Jul 12019 Jul 5

Conference

Conference31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019
CountrySlovenia
CityLjubljana
Period19/7/119/7/5

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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    Cho, H., Huh, J., & Sohn, J. (2019). A bijection between ordinary partitions and self-conjugate partitions with same disparity. Paper presented at 31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019, Ljubljana, Slovenia.