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

被引：4

作者：

Kravitz, Noah ^{[1
]}

机构：

[1] Yale Univ, Grace Hopper Coll, New Haven, CT 06510 USA

来源：

DISCRETE MATHEMATICS | 2019年 / 342卷 / 12期

关键词：

Core partitions; d-distinct parts; Integer compositions; ENUMERATION; CONJECTURE; PROOF; (S;

D O I：

10.1016/j.disc.2019.07.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the number N-d,N- r (s) of (s, s + r)-core integer partitions with d-distinct parts. Our first main result is a proof of a recurrence relation conjectured by Sahin in 2018. We also derive generating functions, asymptotics, and exact formulas for N-d,N- r (s) when r is within d of a multiple of s. Finally, we exhibit a surprising connection to A-restricted compositions. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：14

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