Arithmetic properties of 1-shell totally symmetric plane partitions

Michael D. Hirschhorn, James A. Sellers

Research output: Contribution to journalArticle

1 Citation (Scopus)

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≥0 f(n)qn = 1+ ∑n≥1q3n-2i=0n-2(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.

Original languageEnglish (US)
Pages (from-to)473-478
Number of pages6
JournalBulletin of the Australian Mathematical Society
Volume89
Issue number3
DOIs
StatePublished - Jan 1 2014

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Plane Partitions
Shell
Generating Function
Elementary Functions
Ramanujan
Manipulation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Hirschhorn, Michael D. ; Sellers, James A. / Arithmetic properties of 1-shell totally symmetric plane partitions. In: Bulletin of the Australian Mathematical Society. 2014 ; Vol. 89, No. 3. pp. 473-478.
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Arithmetic properties of 1-shell totally symmetric plane partitions. / Hirschhorn, Michael D.; Sellers, James A.

In: Bulletin of the Australian Mathematical Society, Vol. 89, No. 3, 01.01.2014, p. 473-478.

Research output: Contribution to journalArticle

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