A Self-Conjugate Partition Analog of $(t,t+1)$-Core Partitions with Distinct Parts

Fuente: arXiv
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Main Authors: Xiong, Huan, Yang, Lihong
Format: Preprint
Published: 2025
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author Xiong, Huan
Yang, Lihong
author_facet Xiong, Huan
Yang, Lihong
contents Simultaneous core partitions have been widely studied in the past 20 years. In 2013, Amdeberhan gave several conjectures on the number, the average size, and the largest size of $(t,t+1)$-core partitions with distinct parts, which was proved and generalized by Straub, Xiong, Nath-Sellers, Zaleski-Zeilberger, Paramonov, and many other mathematicians. In this paper, we introduce a proper self-conjugate partition analog of $(t,t+1)$-core partitions with distinct parts, and derive the number, the average size, and the largest size for such core partitions.
format Preprint
id arxiv_https___arxiv_org_abs_2503_00896
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Self-Conjugate Partition Analog of $(t,t+1)$-Core Partitions with Distinct Parts
Xiong, Huan
Yang, Lihong
Combinatorics
Simultaneous core partitions have been widely studied in the past 20 years. In 2013, Amdeberhan gave several conjectures on the number, the average size, and the largest size of $(t,t+1)$-core partitions with distinct parts, which was proved and generalized by Straub, Xiong, Nath-Sellers, Zaleski-Zeilberger, Paramonov, and many other mathematicians. In this paper, we introduce a proper self-conjugate partition analog of $(t,t+1)$-core partitions with distinct parts, and derive the number, the average size, and the largest size for such core partitions.
title A Self-Conjugate Partition Analog of $(t,t+1)$-Core Partitions with Distinct Parts
topic Combinatorics
url https://arxiv.org/abs/2503.00896