TY - JOUR

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

AU - Hirschhorn, Michael D.

AU - Sellers, James A.

N1 - Publisher Copyright:
© 2013 Australian Mathematical Publishing Association Inc.

PY - 2014

Y1 - 2014

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.

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U2 - 10.1017/S0004972713000865

DO - 10.1017/S0004972713000865

M3 - Article

AN - SCOPUS:84912087457

SN - 0004-9727

VL - 89

SP - 473

EP - 478

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 3

ER -