On some questions of Fisk and Br\"and\'en

TL;DR

This paper extends Br"and"en's recent results on polynomial zero distributions and addresses an open question by Fisk, advancing understanding of polynomial behavior under specific operators.

Contribution

It provides an extension to Br"and"en's theorem and answers Fisk's question about polynomial zero distributions under non-linear operators.

Findings

Extended Br"and"en's result on polynomial zeros

Answered Fisk's question on zero distribution

Improved understanding of polynomial behavior under operators

Abstract

P. Br\"and\'en recently proved a conjecture due to S. Fisk, R. P. Stanley, P. R. W. McNamara and B. E. Sagan. In addition, P. Br\"and\'en gave a partial answer to a question posed by S. Fisk regarding the distribution of zeros of polynomials under the action of certain non-linear operators. In this paper, we give an extension to a result of P. Br\"and\'en, and we also answer a question posed by S. Fisk.