Proofs of Two Formulas of Vladeta Jovovic

TL;DR

This paper offers analytic and bijective proofs for formulas related to integer partitions and a sequence from OEIS, expanding understanding of combinatorial identities and their proofs.

Contribution

It introduces new bijective proofs for formulas by Vladeta Jovovic, enhancing combinatorial proof techniques and understanding of integer partitions.

Findings

Provided an analytic proof of Jovovic's formula.

Established a bijective proof of the same formula.

Presented a bijective proof for partitions with fixed differences.

Abstract

In this paper, we first provide an analytic and a bijective proof of a formula stated by Vladeta Jovovic in the OEIS sequence A117989. We also provide a bijective proof of another interesting result stated by him on the same page concerning integer partitions with fixed differences between the largest and smallest parts.