Derivation of the real-rootedness of coordinator polynomials from the Hermite-Biehler theorem

DOI10.1007/s10474-014-0395-3zbMath1324.26021OpenAlexW2081916340MaRDI QIDQ397019

Philip B. Zhang, Matthew H. Y. Xie

Publication date: 14 August 2014

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-014-0395-3

zbMATH Keywords

compatibilitycoordinator polynomialHermite-Biehler theoremreal rootedness

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Real polynomials: location of zeros (26C10) Polynomials and rational functions of one complex variable (30C10) Real polynomials: analytic properties, etc. (26C05)

Related Items (1)

Analytic combinatorics of coordination numbers of cubic lattices

Cites Work

• Unnamed Item
• The real-rootedness and log-concavities of coordinator polynomials of Weyl group lattices
• The roots of the independence polynomial of a clawfree graph
• Obreschkoff's theorem revisited: What convex sets are contained in the set of hyperbolic polynomials?
• Hermite-Biehler, Routh-Hurwitz, and total positivity
• Hermite polynomials
• The Fox-Wright functions and Laguerre multiplier sequences
• Iterated sequences and the geometry of zeros
• Root Polytopes and Growth Series of Root Lattices
• Coordination sequences for root lattices and related graphs
• Low–dimensional lattices. VII. Coordination sequences
• Séries de croissance et séries d'Ehrhart associées aux réseaux de racines
• A new property of a class of Jacobi polynomials

This page was built for publication: Derivation of the real-rootedness of coordinator polynomials from the Hermite-Biehler theorem