Polynomization of the Bessenrodt–Ono Inequality
Polynomization of the Bessenrodt–Ono Inequality
Abstract In this paper, we investigate a generalization of the Bessenrodt–Ono inequality by following Gian–Carlo Rota’s advice in studying problems in combinatorics and number theory in terms of roots of polynomials. We consider the number of k -colored partitions of n as special values of polynomials $$P_n(x)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> …