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

Hyunsoo Cho; Jisun Huh; Jaebum Sohn

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

Hyunsoo Cho, Jisun Huh, Jaebum Sohn

Department of Mathematics

Research output: Contribution to conference › Paper › peer-review

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 language	English
Publication status	Published - 2019
Event	31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019 - Ljubljana, Slovenia Duration: 2019 Jul 1 → 2019 Jul 5

Conference

Conference	31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019
Country/Territory	Slovenia
City	Ljubljana
Period	19/7/1 → 19/7/5

Bibliographical note

Publisher Copyright:
© FPSAC 2019 - 31st International Conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Cite this

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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.",

keywords = "Hook length, Partition, Self-conjugate partition, Simultaneous core partition",

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TY - CONF

T1 - A bijection between ordinary partitions and self-conjugate partitions with same disparity

AU - Cho, Hyunsoo

AU - Huh, Jisun

AU - Sohn, Jaebum

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Hook length

KW - Partition

KW - Self-conjugate partition

KW - Simultaneous core partition

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UR - http://www.scopus.com/inward/citedby.url?scp=85087881914&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:85087881914

T2 - 31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019

Y2 - 1 July 2019 through 5 July 2019

ER -

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

Abstract

Conference

Bibliographical note

All Science Journal Classification (ASJC) codes

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