Integrals, partitions and MacMahon's theorem
2007 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 114, no 3, 545-554 p.Article in journal (Refereed) Published
In two previous papers, the study of partitions with short sequences has been developed both for its intrinsic interest and for a variety of applications. The object of this paper is to extend that study in various ways. First, the relationship of partitions with no consecutive integers to a theorem of MacMahon and mock theta functions is explored independently. Secondly, we derive in a succinct manner a relevant definite integral related to the asymptotic enumeration of partitions with short sequences. Finally, we provide the generating function for partitions with no sequences of length K and part exceeding N.
Place, publisher, year, edition, pages
2007. Vol. 114, no 3, 545-554 p.
partition identities, partition generating functions, partitions without consecutive parts, MacMahon's theorem, mock theta function
IdentifiersURN: urn:nbn:se:kth:diva-16537DOI: 10.1016/j.jcta.2006.06.010ISI: 000245523400009ScopusID: 2-s2.0-33846811254OAI: oai:DiVA.org:kth-16537DiVA: diva2:334579
QC 201005252010-08-052010-08-05Bibliographically approved