ARITHMETIC PROPERTIES OF 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS

被引：12

作者：

Hirschhorn, Michael D. ^{[1
]}

Sellers, James A. ^{[2
]}

机构：

[1] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2014年 / 89卷 / 03期

关键词：

partition; totally symmetric plane partition; TSPP; generating function; congruence;

D O I：

10.1017/S0004972713000865

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Blecher ['Geometry for totally symmetric plane partitions (TSPPs) with self-conjugate main diagonal', Util. Math. 88 (2012), 223-235] defined the combinatorial objects known as 1-shell totally symmetric plane partitions of weight n. He also proved that the generating function for f (n); the number of 1-shell totally symmetric plane partitions of weight n, is given by Sigma f (n)q(n) = 1 + Sigma q(3n-2) Pi (1 + q(6i+3)) n >= 0 n >= 1 i=0 In this brief note, we prove a number of arithmetic properties satisfied by f (n) using elementary generating function manipulations and well-known results of Ramanujan and Watson.

引用

页码：473 / 478

页数：6

共 7 条

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STEMBRIDGE, JR
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