The largest size of an (s,s + 1)-core partition with parts of the same parity-Reference-Cited by-同舟云学术

The largest size of an (s,s + 1)-core partition with parts of the same parity

Published:2020-09-30 Issue:03 Volume:17 Page:699-712
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Nam Hayan¹,Yu Myungjun²^ORCID

Affiliation:

1. Department of Mathematics, Duksung Women’s University, Seoul 01370, Republic of Korea

2. Center for Mathematical Challenges, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea

Abstract

Finding the largest size of a partition under certain restrictions has been an interesting subject to study. For example, it is proved by Olsson and Stanton that for two coprime integers [Formula: see text] and [Formula: see text], the largest size of an [Formula: see text]-core partition is [Formula: see text]. Xiong found a formula for the largest size of a [Formula: see text]-core partitions with distinct parts. In this paper, we find an explicit formula for the largest size of an [Formula: see text]-core partition such that all parts are odd (or even).

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179304212040014X

Reference9 articles.

1. Partitions which are simultaneously t1- and t2-core

2. A bijective proof of Amdeberhan’s conjecture on the number of(s,s+2)-core partitions with distinct parts

3. Johnson’s bijections and their application to counting simultaneous core partitions

4. Lattice Points and Simultaneous Core Partitions

5. On the number of simultaneous core partitions with d-distinct parts

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