In this paper we study the largest parts in integer partitions according to multiplicities and part sizes. Firstly we investigate various properties of the multiplicities of the largest parts. We then consider the sum of the m largest parts - first as distinct parts and then including multiplicities. Finally, we find the generating function for the sum of the m largest parts of a partition, i.e., the first m parts of a weakly decreasing sequence of parts.
|Number of pages||16|
|Journal||Australasian Journal of Combinatorics|
|State||Published - 2016|
Bibliographical noteFunding Information:
This material is based upon work supported by the National Research Foundation under grant numbers 89147, 86329 and 81021.
© 2016, University of Queensland. All rights reserved.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics