1 research outputs found
The Real-Rootedness and Log-concavities of Coordinator Polynomials of Weyl Group Lattices
It is well-known that the coordinator polynomials of the classical root
lattice of type and those of type 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 . We also find the coordinator polynomials of type
are not real-rooted in general. As a conclusion, we obtain that all
coordinator polynomials of Weyl group lattices are log-concave.Comment: 8 page