TY - JOUR
T1 - Arithmetic properties of 1-shell totally symmetric plane partitions
AU - Hirschhorn, Michael D.
AU - Sellers, James A.
PY - 2014/6
Y1 - 2014/6
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 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 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 - 10.1017S0004972713000865
DO - 10.1017S0004972713000865
M3 - Article
AN - SCOPUS:84902081349
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 -