Core partitions with distinct parts

2015/08/31 by Huan Xiong, Xiong, Huan · 2 citations
Mathematics · #05A17 #11P81 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1508.07918

openalex publication_date 2015/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Simultaneous core partitions have attracted much attention since Anderson's work on the number of (t₁,t₂)-core partitions. In this paper we focus on simultaneous core partitions with distinct parts. The generating function of t-core partitions with distinct parts is obtained. We also prove the results on the number, the largest size and the average size of (t, t + 1)-core partitions. This gives a complete answer to a conjecture of Amdeberhan, which is partly and independently proved by Straub, Nath and Sellers, and Zaleski recently.

Citations

• Theorems, Problems and Conjectures

Cited by

• Simultaneous cores with restrictions and a question of Zaleski and\n Zeilberger
• Bijections between t-Core Partitions and t-Tuples

Related

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• A Self-Conjugate Partition Analog of (t,t+1)-Core Partitions with Distinct Parts
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• On the largest size of (t,t+1,..., t+p)-core partitions
• Bijections between t-Core Partitions and t-Tuples