1-Shell totally symmetric plane partitions (TSPPs) modulo powers of 5

被引：7

作者：

Chern, Shane ^{[1
]}

机构：

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

来源：

RAMANUJAN JOURNAL | 2021年 / 55卷 / 02期

关键词：

Partitions; 1-Shell TSPPs; Congruences; Powers of 5;

D O I：

10.1007/s11139-020-00306-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let s(n) be the number of 1-shell totally symmetric plane partitions (TSPPs) of n. In this paper, an infinite family of congruences modulo powers of 5 for s(n) will be deduced through an elementary approach. Namely, s(2 . 5(2 alpha-1)n + 5(2 alpha-1)) equivalent to 0 (mod 5(alpha)).

引用

页码：713 / 731

页数：19

共 31 条

[1] 1-Shell totally symmetric plane partitions (TSPPs) modulo powers of 5
Shane Chern
The Ramanujan Journal, 2021, 55 : 713 - 731
[2] A NEW CONGRUENCE MODULO 25 FOR 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS
Xia, Ernest X. W.
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2015, 91 (01) : 41 - 46
[3] ARITHMETIC PROPERTIES OF 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS
Hirschhorn, Michael D.
Sellers, James A.
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2014, 89 (03) : 473 - 478
[4] NEW INFINITE FAMILIES OF CONGRUENCES MODULO 4 AND 8 FOR 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS
Yao, Olivia X. M.
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2014, 90 (01) : 37 - 46
[5] Geometry of totally symmetric plane partitions (TSPPs) with self-conjugate main diagonal
Blecher, Aubrey
UTILITAS MATHEMATICA, 2012, 88 : 223 - 235
[6] Cubic partitions modulo powers of 5
Michael D. Hirschhorn
The Ramanujan Journal, 2020, 51 : 67 - 84
[7] Cubic partitions modulo powers of 5
Hirschhorn, Michael D.
RAMANUJAN JOURNAL, 2020, 51 (01): : 67 - 84
[8] Partitions into Distinct Parts Modulo Powers of 5
Chern, Shane
Hirschhorn, Michael D.
ANNALS OF COMBINATORICS, 2019, 23 (3-4) : 659 - 682
[9] Partitions into Distinct Parts Modulo Powers of 5
Shane Chern
Michael D. Hirschhorn
Annals of Combinatorics, 2019, 23 : 659 - 682
[10] The 2-adic valuation of plane partitions and totally symmetric plane partitions
Keith, William J.
ELECTRONIC JOURNAL OF COMBINATORICS, 2012, 19 (01):

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