On the largest size of a partition that is both s-core and t-core

JOURNAL OF NUMBER THEORY

卷:129

Article

Tripathi, Amitabha

关键词: Partition;    Hook;    Hook number;    t-Core;    Structure number;    t-Abacus;   

DOI  :  10.1016/j.jnt.2008.08.009

来源: Elsevier

【 摘 要 】

Text. Let s, t be relatively prime positive integers. We prove a conjecture of Aukerman, Kane and Sze regarding the largest size of a partition that is simultaneously s-core and t-core by solving an equivalent problem concerning sets S of positive integers with the property that for n is an element of S, n-s is an element of S whenever n >= s and n-t is an element of S whenever n >= t. Video. For a video summary of this paper, please visit http://www.youtube.com/watch?v=o10Eug8LryU. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free