Submultiplicative polynomials in combinatorics

The Ramanujan Journal, vol. 71

Abstract

Abstract For normalized sequences $$\left( g(n)\right) _{n\in \mathbb {N}}$$ g ( n ) n ∈ N we consider recursively defined polynomials $$P_n^g(x)$$ P n g ( x ) . In this paper we study their submultiplicative property, viewed as a Bessenrodt–Ono type inequality for the partition function, and provide an effective criterion for establishing it.

Authors 4

1. Krystian Gajdzica corresponding

   Jagiellonian University

   Affiliation as printed

   Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348, Kraków, Poland

2. Bernhard E. Heim

   University of Cologne

   Affiliation as printed

   Faculty of Mathematical and Natural Sciences, Mathematical Institute, University of Cologne, Weyertal 86–90, 50931, Cologne, Germany

3. Markus Neuhauser Aachen Lehrstuhl für Geometrie und Analysis

   Kutaisi International University · RWTH Aachen University

   Affiliation as printed

   Kutaisi International University, 5/7, Youth Avenue, 4600, Kutaisi, Georgia

   Lehrstuhl für Geometrie und Analysis, RWTH Aachen University, 52056, Aachen, Germany

4. Błażej Żmija

   AGH University of Krakow

   Affiliation as printed

   Faculty of Applied Mathematics, AGH University of Krakow, Al. Mickiewicza 30, 30-059, Kraków, Poland