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A NEW CONGRUENCE MODULO 25 FOR 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS

Part of: Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  08 October 2014

ERNEST X. W. XIA
ERNEST X. W. XIA*
Affiliation:
Department of Mathematics, Jiangsu University, Zhenjiang, Jiangsu 212013, PR China email [email protected]
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Abstract

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For 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 $f(250n+125)\equiv 0\ (\text{mod\ 25}).$

Keywords

congruence1-shell totally symmetric plane partitionsTSPP

MSC classification

Primary: 11P83: Partitions; congruences and congruential restrictions 05A17: Partitions of integers
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 1 , February 2015 , pp. 41 - 46
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

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