The real-rootedness and log-concavities of coordinator polynomials of Weyl group lattices

Authors:
David G. L. Wang;Tongyuan Zhao
Affiliations:
Beijing International Center for Mathematical Research, Peking University, Beijing 100871, PR China;School of Mathematics, LMAM, Peking University, Beijing 100871, PR China
Venue:
European Journal of Combinatorics
Year:
2013

Citing 5
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Abstract

It is well-known that the coordinator polynomials of the classical root lattice of type A"n and those of type C"n are real-rooted. They can be obtained, either by the Aissen-Schoenberg-Whitney theorem, or from their recurrence relations. In this paper, we develop a trigonometric substitution approach which can be used to establish the real-rootedness of coordinator polynomials of type D"n. We also find the coordinator polynomials of type B"n are not real-rooted in general. As a conclusion, we obtain that all coordinator polynomials of Weyl group lattices are log-concave.