Proof of a Nonnegativity Conjecture of Merca

Abstract

Merca recently studied the partitions of n in which no part appears d or more times, and connected an infinite family of linear inequalities related to these partitions to the nonnegativity of coefficients of a certain infinite series. In this paper, we prove Merca’s conjecture. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2026.