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- W2952203684 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." @default.
- W2952203684 created "2019-06-27" @default.
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- W2952203684 date "2011-06-19" @default.
- W2952203684 modified "2023-10-18" @default.
- W2952203684 title "The Real-Rootedness and Log-concavities of Coordinator Polynomials of Weyl Group Lattices" @default.
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- W2952203684 doi "https://doi.org/10.48550/arxiv.1106.3765" @default.
- W2952203684 hasPublicationYear "2011" @default.
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