The number of self-conjugate core partitions

JOURNAL OF NUMBER THEORY

卷:133

Article

Hanusa, Christopher R. H.¹  Nath, Rishi² 

[1] CUNY Queens Coll, Dept Math, Flushing, NY 11367 USA

[2] CUNY York Coll, Dept Math & Comp Sci, Jamaica, NY 11451 USA

关键词: Core partition;    t-Core;    t-Quotient;    Self-conjugate;    Positivity;    Monotonicity;   

DOI  :  10.1016/j.jnt.2012.08.017

来源: Elsevier

【 摘 要 】

A conjecture on the monotonicity of t-core partitions in an article of Stanton [Dennis Stanton, Open positivity conjectures for integer partitions, Trends Math. 2 (1999) 19-25] has been the catalyst for much recent research on t-core partitions. We conjecture Stanton-like monotonicity results comparing self-conjugate (t + 2)- and t-core partitions of n. We obtain partial results toward these conjectures for values of t that are large with respect to n, and an application to the block theory of the symmetric and alternating groups. To this end we prove formulas for the number of self-conjugate t-core partitions of n as a function of the number of self-conjugate partitions of smaller n. Additionally, we discuss the positivity of self-conjugate 6-core partitions and introduce areas for future research in representation theory, asymptotic analysis, unimodality, and numerical identities and inequalities. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free