TY - JOUR
T1 - Integrals, partitions and MacMahon's Theorem
AU - Andrews, George
AU - Eriksson, Henrik
AU - Petrov, Fedor
AU - Romik, Dan
N1 - Funding Information:
E-mail addresses: [email protected] (G. Andrews), [email protected] (H. Eriksson), [email protected] (F. Petrov), [email protected] (D. Romik). 1 Research partially supported by NSF grant DMS 0457003. 2 Research supported by grants CRDF RUM1-2622-CT04, NSh2251-2003.1. 3 Research supported by NSF-FRG grant #0244479.
PY - 2007/4
Y1 - 2007/4
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.
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U2 - 10.1016/j.jcta.2006.06.010
DO - 10.1016/j.jcta.2006.06.010
M3 - Article
AN - SCOPUS:33846811254
SN - 0097-3165
VL - 114
SP - 545
EP - 554
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
IS - 3
ER -