Submultiplicative Polynomials in Combinatorics

Krystian Gajdzica; Bernhard Heim; Markus Neuhauser; Błażej Żmija

Submultiplicative Polynomials in Combinatorics

Combinatorics 2026-07-13 v1 Number Theory

Authors: Krystian Gajdzica , Bernhard Heim , Markus Neuhauser , Błażej Żmija

Abstract

For normalized sequences $\left(g(n)\right)_{n\in\mathbb{N}}$ we consider recursively defined polynomials $P_n^g(x)$ . 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.

Cite

@article{arxiv.2607.11568,
  title  = {Submultiplicative Polynomials in Combinatorics},
  author = {Krystian Gajdzica and Bernhard Heim and Markus Neuhauser and Błażej Żmija},
  journal= {arXiv preprint arXiv:2607.11568},
  year   = {2026}
}

Comments

11 pages