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Integrals, partitions and MacMahon's Theorem. / Andrews, George; Eriksson, Henrik; Petrov, Fedor; Romik, Dan.

In: Journal of Combinatorial Theory. Series A, Vol. 114, No. 3, 01.04.2007, p. 545-554.

Research output: Contribution to journal › Article › peer-review

Harvard

Andrews, G, Eriksson, H, Petrov, F & Romik, D 2007, 'Integrals, partitions and MacMahon's Theorem', Journal of Combinatorial Theory. Series A, vol. 114, no. 3, pp. 545-554. https://doi.org/10.1016/j.jcta.2006.06.010

APA

Andrews, G., Eriksson, H., Petrov, F., & Romik, D. (2007). Integrals, partitions and MacMahon's Theorem. Journal of Combinatorial Theory. Series A, 114(3), 545-554. https://doi.org/10.1016/j.jcta.2006.06.010

Vancouver

Andrews G, Eriksson H, Petrov F, Romik D. Integrals, partitions and MacMahon's Theorem. Journal of Combinatorial Theory. Series A. 2007 Apr 1;114(3):545-554. https://doi.org/10.1016/j.jcta.2006.06.010

Author

Andrews, George ; Eriksson, Henrik ; Petrov, Fedor ; Romik, Dan. / Integrals, partitions and MacMahon's Theorem. In: Journal of Combinatorial Theory. Series A. 2007 ; Vol. 114, No. 3. pp. 545-554.

BibTeX

@article{216f341d9cdf47fe8cdc00c7469130a3,
title = "Integrals, partitions and MacMahon's Theorem",
abstract = "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.",
keywords = "MacMahon's Theorem, Mock theta function, Partition generating functions, Partition identities, Partitions without consecutive parts",
author = "George Andrews and Henrik Eriksson and Fedor Petrov and Dan Romik",
year = "2007",
month = apr,
day = "1",
doi = "10.1016/j.jcta.2006.06.010",
language = "English",
volume = "114",
pages = "545--554",
journal = "Journal of Combinatorial Theory - Series A",
issn = "0097-3165",
publisher = "Elsevier",
number = "3",

}

RIS

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 -

ID: 47858851