New infinite families of congruences modulo 4 and 8 for 1-shell totally symmetric plane partitions

Authors

  • O. X. M. Yao Jiangsu University

Keywords:

congruence, 1-shell totally symmetric plane partition, TSPP

Abstract

In 2012, Blecher [‘Geometry for totally symmetric plane partitions (TSPPs) with self-conjugate main diagonal’, Util. Math. 88 (2012), 223–235] introduced a special class of totally symmetric plane partitions, called 1-shell totally symmetric plane partitions. Let f(n) denote the number of 1-shell totally symmetric plane partitions of weight n. More recently, Hirschhorn and Sellers [‘Arithmetic properties of 1-shell totally symmetric plane partitions’, Bull. Aust. Math. Soc. to appear. Published online 27 September 2013] discovered a number of arithmetic properties satisfied by f(n). In this paper, employing some results due to Cui and Gu [‘Arithmetic properties of l-regular partitions’, Adv. Appl. Math. 51 (2013), 507–523], and Hirschhorn and Sellers, we prove several new infinite families of congruences modulo 4 and 8 for 1-shell totally symmetric plane partitions. For example, we find that, for n≥0 and α≥1, \[ f(8 \times 5^{2\alpha} n+39\times 5^{2\alpha-1})\equiv 0 \ ({\rm mod \ 8}). \] DOI: 10.1017/S0004972713001160

Published

2014-06-03

Issue

Vol. 90 No. 1 (2014)

Section

Articles
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