Year: 2026
Type: preprint
Abstract: We prove the real-rootedness conjecture of Lin, Ma, Ma, and Zhou (2021) for multiset Eulerian-Narayana polynomials, including simplicity and negativity of all zeros after removing the factor t. Using a forest decomposition and Lagrange inversion, we derive a differential formula and a first-order factorization of the differential operator. We use these factors to show that the nonconstant gamma-coefficients and ordered gamma-zeros are nondecreasing, with corresponding bounds given by the Narayana and Eulerian polynomials. The same factorization gives totally nonnegative coefficient transition matrices. We also prove strict interlacing of the zeros of generating polynomials arising from adjacent columns of the transition matrices.
Source: arXiv (Cornell University)
Authors: Zhang, Philip B., Zhao, Tongyuan
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G4338915643, G6545595343, G7610362479
OpenAlex ID: W7216501068