### 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)q^{n} = 1+ ∑_{n≥1}q^{3n-2} ∏_{i=0}^{n-2}(1+q^{6i+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 language | English (US) |
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Pages (from-to) | 473-478 |

Number of pages | 6 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 89 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2014 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Hirschhorn, M. D., & Sellers, J. A. (2014). Arithmetic properties of 1-shell totally symmetric plane partitions.

*Bulletin of the Australian Mathematical Society*,*89*(3), 473-478. https://doi.org/10.1017/S0004972713000865