Combinatorial Proof of a Partition Inequality of Bessenrodt-Ono

Combinatorial Proof of a Partition Inequality of Bessenrodt-Ono We provide a combinatorial proof of the inequality $${p(a)p(b) > p(a+b)}$$ p ( a ) p ( b ) > p ( a + b ) , where p(n) is the partition function and a, $${b > 1}$$ b > 1 are integers satisfying $${a+b > 9}$$ a + b > 9 . This problem was posed by Bessenrodt and Ono who used the inequality to study a new multiplicative property of an extended partition function [Ann. Combin. 20, 59–64 (2016)]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Combinatorics Springer Journals

Combinatorial Proof of a Partition Inequality of Bessenrodt-Ono

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Mathematics; Combinatorics
ISSN
0218-0006
eISSN
0219-3094
D.O.I.
10.1007/s00026-017-0358-9
Publisher site
See Article on Publisher Site

Abstract

We provide a combinatorial proof of the inequality $${p(a)p(b) > p(a+b)}$$ p ( a ) p ( b ) > p ( a + b ) , where p(n) is the partition function and a, $${b > 1}$$ b > 1 are integers satisfying $${a+b > 9}$$ a + b > 9 . This problem was posed by Bessenrodt and Ono who used the inequality to study a new multiplicative property of an extended partition function [Ann. Combin. 20, 59–64 (2016)].

Journal

Annals of CombinatoricsSpringer Journals

Published: Jul 21, 2017

References

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