Partitions with short sequences and mock theta functions
- 16 February 2005
- journal article
- research article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences of the United States of America
- Vol. 102 (13), 4666-4671
- https://doi.org/10.1073/pnas.0500218102
Abstract
P. A. MacMahon was the first to examine integer partitions in which consecutive integers were not allowed as parts. Such partitions may be described as having sequences of length 1. Recently it was shown that partitions containing no sequences of consecutive integers of length k are of interest in seemingly unrelated problems concerning threshold growth models. The object now is to develop the subject intrinsically to both provide deeper understanding of the theory and application of partitions and reveal the surprising role of Ramanujan's mock theta functions.This publication has 6 references indexed in Scilit:
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