Proc. Japan Acad. Ser. A Math. Sci. 99 (5), 33-36, (May 2023) DOI: 10.3792/pjaa.99.007
KEYWORDS: Gaussian polynomial, $q$-log-concavity, $q$-unimodality, nonnegativity, 05A20, 05A10, 11B65
We answer a nonnegativity problem of G. E. Andrews and D. Newman by the $q$-unimodality of Gaussian polynomials. Some new considerations of the $q$-log-concavity and $q$-unimodality of Gaussian polynomials from a purely partition-theoretic perspective will also be presented.