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|
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics