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abstract

Further developments in MacMahon's partition analysis (abstract only)

Published: 25 July 2008 Publication History

Abstract

P.A. MacMahon developed a calculus for producing generating functions of partitions constrained by linear inequalities relating the various parts of the partitions. Recently we have used MacMahon's method to find new classes of partitions whose generating functions are modular forms (Acta Arith., 126(2007), 281-294), and we have retrieved MacMahon's original project which was to prove his generating function formula for plane partitions. We shall report briefly on these topics and indicate new areas for exploration. In particular, we shall consider the modification of MacMahon's methods in which the inequalities relating the various parts of the partition take into account congruence constraints on the parts.

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cover image ACM Communications in Computer Algebra
ACM Communications in Computer Algebra  Volume 42, Issue 1-2
March/June 2008
136 pages
ISSN:1932-2232
EISSN:1932-2240
DOI:10.1145/1394042
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 25 July 2008
Published in SIGSAM-CCA Volume 42, Issue 1-2

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