On the real-rootedness of the Eulerian transformation
From MaRDI portal
Publication:6425142
arXiv2302.00754MaRDI QIDQ6425142
Author name not available (Why is that?)
Publication date: 1 February 2023
Abstract: The Eulerian transformation is the linear operator on polynomials in one variable with real coefficients which maps the powers of this variable to the corresponding Eulerian polynomials. The derangement transformation is defined similarly. Br"and'en and Jochemko have conjectured that the Eulerian transforms of a class of polynomials with nonnegative coefficients, which includes those having all their roots in the interval , have only real zeros. This conjecture is proven in this paper. More general transformations are introduced in the combinatorial-geometric context of uniform triangulations of simplicial complexes, where Eulerian and derangement transformations arise in the special case of barycentric subdivision, and are shown to have strong unimodality and gamma-positivity properties. General real-rootedness conjectures for these transformations, which unify various results and conjectures in the literature, are also proposed.
No records found.
This page was built for publication: On the real-rootedness of the Eulerian transformation
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6425142)
