Details
Originalsprache | Englisch |
---|---|
Seiten (von - bis) | 231-250 |
Seitenumfang | 20 |
Fachzeitschrift | Annals of combinatorics |
Jahrgang | 20 |
Ausgabenummer | 2 |
Frühes Online-Datum | 16 März 2016 |
Publikationsstatus | Veröffentlicht - Juni 2016 |
Abstract
In a previous paper of the second author with K. Ono, surprising multiplicative properties of the partition function were presented. Here, we deal with k-regular partitions. Extending the generating function for k-regular partitions multiplicatively to a function on k-regular partitions, we show that it takes its maximum at an explicitly described small set of partitions, and can thus easily be computed. The basis for this is an extension of a classical result of Lehmer, from which an inequality for the generating function for k-regular partitions is deduced which seems not to have been noticed before.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Diskrete Mathematik und Kombinatorik
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in: Annals of combinatorics, Jahrgang 20, Nr. 2, 06.2016, S. 231-250.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Multiplicative Properties of the Number of k-Regular Partitions
AU - Beckwith, Olivia
AU - Bessenrodt, Christine
PY - 2016/6
Y1 - 2016/6
N2 - In a previous paper of the second author with K. Ono, surprising multiplicative properties of the partition function were presented. Here, we deal with k-regular partitions. Extending the generating function for k-regular partitions multiplicatively to a function on k-regular partitions, we show that it takes its maximum at an explicitly described small set of partitions, and can thus easily be computed. The basis for this is an extension of a classical result of Lehmer, from which an inequality for the generating function for k-regular partitions is deduced which seems not to have been noticed before.
AB - In a previous paper of the second author with K. Ono, surprising multiplicative properties of the partition function were presented. Here, we deal with k-regular partitions. Extending the generating function for k-regular partitions multiplicatively to a function on k-regular partitions, we show that it takes its maximum at an explicitly described small set of partitions, and can thus easily be computed. The basis for this is an extension of a classical result of Lehmer, from which an inequality for the generating function for k-regular partitions is deduced which seems not to have been noticed before.
KW - generating function for k-regular partitions
KW - k-regular partitions
KW - partition function
KW - partitions
UR - http://www.scopus.com/inward/record.url?scp=84962615516&partnerID=8YFLogxK
U2 - 10.1007/s00026-016-0309-x
DO - 10.1007/s00026-016-0309-x
M3 - Article
AN - SCOPUS:84962615516
VL - 20
SP - 231
EP - 250
JO - Annals of combinatorics
JF - Annals of combinatorics
SN - 0218-0006
IS - 2
ER -