2020/10/12 by Arjun Pawar, Pawar, Arjun
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #History and Overview (math.HO)
paper · pdf · doi:10.48550/arxiv.2010.06380
openalex publication_date 2020/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we present a short, non-exhaustive study of an important and well-known property of combinatorial sequences - unimodality. We shall have a look at a sample of classical results on unimodality and related properties, and then proceed to understand the unimodality of the Gaussian polynomial in more detail. We will look at an outline of O'Hara's proof of the unimodality of the Gaussian polynomial. In order to grasp the challenge of the problem of obtaining an injective proof of the unimodality of the Gaussian polynomial (which is still an open question), we make several attempts and understand where these attempts fail.