A NEW CONGRUENCE MODULO 25 FOR 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS
2014 ◽
Vol 91
(1)
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pp. 41-46
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AbstractFor any positive integer $n$, let $f(n)$ denote the number of 1-shell totally symmetric plane partitions of $n$. Recently, Hirschhorn and Sellers [‘Arithmetic properties of 1-shell totally symmetric plane partitions’, Bull. Aust. Math. Soc.89 (2014), 473–478] and Yao [‘New infinite families of congruences modulo 4 and 8 for 1-shell totally symmetric plane partitions’, Bull. Aust. Math. Soc.90 (2014), 37–46] proved a number of congruences satisfied by $f(n)$. In particular, Hirschhorn and Sellers proved that $f(10n+5)\equiv 0\ (\text{mod}\ 5)$. In this paper, we establish the generating function of $f(30n+25)$ and prove that $f(250n+125)\equiv 0\ (\text{mod\ 25}).$
2013 ◽
Vol 89
(3)
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pp. 473-478
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2009 ◽
Vol DMTCS Proceedings vol. AK,...
(Proceedings)
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Keyword(s):
2014 ◽
Vol 90
(1)
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pp. 37-46
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2015 ◽
Vol DMTCS Proceedings, 27th...
(Proceedings)
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1961 ◽
Vol 13
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pp. 217-220
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Keyword(s):
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2015 ◽
Vol 11
(04)
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pp. 1063-1072
2015 ◽
Vol 30
(33)
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pp. 1550202
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