Self-conjugate partitions with the same disparity

Hyunsoo Cho, Ji Sun Huh, Jaebum Sohn

Research output: Contribution to journalArticlepeer-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 languageEnglish
Article number111806
JournalDiscrete Mathematics
Volume343
Issue number5
DOIs
Publication statusPublished - 2020 May

Bibliographical note

Funding Information:
The authors are grateful to Byungchan Kim and the referee for their careful reading and valuable comments on this paper. The second named author's work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (2016R1A5A1008055). The third named author's work was supported by the National Research Foundation of Korea (NRF)NRF-2017R1A2B4009501.

Funding Information:
The authors are grateful to Byungchan Kim and the referee for their careful reading and valuable comments on this paper. The second named author’s work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( 2016R1A5A1008055 ). The third named author’s work was supported by the National Research Foundation of Korea (NRF) NRF-2017R1A2B4009501 .

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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