On simultaneous s-cores/t-cores

被引：8

作者：

Aukerman, David

Kane, Ben ^{[1
]}

Sze, Lawrence ^{[2
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] Calif Polytech State Univ San Luis Obispo, Dept Math, San Luis Obispo, CA 93407 USA

来源：

DISCRETE MATHEMATICS | 2009年 / 309卷 / 09期

基金：

美国国家科学基金会;

关键词：

Partitions; t-cores; Generating functions; P-BLOCKS; PARTITIONS; RESIDUE;

D O I：

10.1016/j.disc.2008.06.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the authors investigate the question of when a partition of n is an element of N is an s-core and also a t-core when s and t are not relatively prime. A characterization of all such s/t-cores is given, as well as a generating function dependent upon the polynomial generating functions for s/t-cores when s and t are relatively prime. Furthermore, characterizations and generating functions are given for s/t-cores which are self-conjugate and also for (e, r)/(e', r)-cores. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：2712 / 2720

页数：9

共 18 条

[1] Partitions which are simultaneously t1- and t2-core [J].