ARITHMETIC PROPERTIES OF 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS
2013 ◽
Vol 89
(3)
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pp. 473-478
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Keyword(s):
AbstractBlecher [‘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$$\begin{eqnarray*}\displaystyle \sum _{n\geq 0}f(n){q}^{n} = 1+ \sum _{n\geq 1}{q}^{3n- 2} \prod _{i= 0}^{n- 2} (1+ {q}^{6i+ 3} ).\end{eqnarray*}$$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.
2014 ◽
Vol 90
(1)
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pp. 37-46
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2014 ◽
Vol 91
(1)
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pp. 41-46
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2009 ◽
Vol DMTCS Proceedings vol. AK,...
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1967 ◽
Vol 67
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pp. 185-195
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2015 ◽
Vol 11
(05)
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pp. 1463-1476
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Keyword(s):
1905 ◽
Vol 40
(3)
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pp. 615-629
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1991 ◽
Vol 43
(3)
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pp. 506-525
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2019 ◽
Vol 149
(03)
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pp. 831-847
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