Arithmetic properties of 1--shell totally symmetric plane partitions

Authors

  • M. D. Hirschhorn UNSW
  • J. A. Sellers Penn State University

Keywords:

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

Abstract

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 ∑n≥0f(n)qn=1+∑n≥1q3n−2n−2∏i=0(1+q6i+3). 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. DOI: 10.1017/S0004972713000865

Published

2014-03-25

Issue

Vol. 89 No. 3 (2014)

Section

Articles
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