TY - JOUR

T1 - Integrals, partitions and MacMahon's Theorem

AU - Andrews, George

AU - Eriksson, Henrik

AU - Petrov, Fedor

AU - Romik, Dan

PY - 2007/4/1

Y1 - 2007/4/1

N2 - 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.

AB - 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.

KW - MacMahon's Theorem

KW - Mock theta function

KW - Partition generating functions

KW - Partition identities

KW - Partitions without consecutive parts

UR - http://www.scopus.com/inward/record.url?scp=33846811254&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2006.06.010

DO - 10.1016/j.jcta.2006.06.010

M3 - Article

AN - SCOPUS:33846811254

VL - 114

SP - 545

EP - 554

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 3

ER -