On sets represented by partitions

TL;DR

This paper introduces a lemma that helps establish upper bounds on the number of sets represented by integer partitions, improving previous bounds and advancing understanding of partition-related set representations.

Contribution

The paper presents a new lemma that enables tighter upper bounds on the number of sets represented by integer partitions, enhancing existing combinatorial bounds.

Findings

Derived an improved upper bound for sets represented by integer partitions

Established a useful lemma for bounding partition-related set counts

Enhanced understanding of the relationship between partitions and set representations

Abstract

We prove a lemma that is useful to get upper bounds for the number of partitions without a given subsum. From this we can deduce an improved upper bound for the number of sets represented by the (unrestricted or into unequal parts) partitions of an integer n.