# 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

, Volume 21 (3) – Jul 21, 2017
7 pages

/lp/springer_journal/combinatorial-proof-of-a-partition-inequality-of-bessenrodt-ono-bR9hzdsIBY
Publisher
Springer International Publishing
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

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