### 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) |
---|---|

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 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Bulletin of the Australian Mathematical Society*,

*89*(3), 473-478. https://doi.org/10.1017/S0004972713000865

}

*Bulletin of the Australian Mathematical Society*, vol. 89, no. 3, pp. 473-478. https://doi.org/10.1017/S0004972713000865

**Arithmetic properties of 1-shell totally symmetric plane partitions.** / Hirschhorn, Michael D.; Sellers, James A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Arithmetic properties of 1-shell totally symmetric plane partitions

AU - Hirschhorn, Michael D.

AU - Sellers, James A.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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-2 ∏i=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.

AB - 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-2 ∏i=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.

UR - http://www.scopus.com/inward/record.url?scp=84912087457&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84912087457&partnerID=8YFLogxK

U2 - 10.1017/S0004972713000865

DO - 10.1017/S0004972713000865

M3 - Article

AN - SCOPUS:84912087457

VL - 89

SP - 473

EP - 478

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

SN - 0004-9727

IS - 3

ER -