Distinct Partitions and Some q-Binomial Summation Identities

2022/06/09 by Kronenburg, M. J.
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2206.05062

Abstract

The partition functions P(n,m,p), the number of integer partitions of n into exactly m parts with each part at most p, and Q(n,m,p), the number of integer partitons of n into exactly m distinct parts with each part at most p, are related by double summation identities which follow from their generating functions. From these identities and some identities from an earlier paper, some other identities involving distinct partitions and some q-binomial summation identities are proved, and from these follow some combinatorial identities.

Related

• The combinatorics of identities involving overpartitions with distinct parts
• Combinatorial Formula for the Partition Function
• Computation of q-Binomial Coefficients with the P(n,m) Integer Partition Function
• Distinct parts partitions without sequences
• Identities involving partitions with distinct odd parts and no parts congruent to 2 mod 4