Turán inequalities for k-th power partition functions

Abstract

The k-th power partition function counts the number of ways that an integer can be written as a sum of perfect k-th powers, a restriction of the well known partition function. Many restricted partition functions have recently been proven to satisfy the higher order the Turán inequalities. This paper shows that the k-th power partition function likewise satisfies these inequalities. In particular, we prove a conjecture by Ulas, improving the upper and lower bounds given in his inequality.