Abstract
In this paper, we study the Ehrhart polynomial of the dual of the root polytope of type C of dimension d, denoted by \(C_d^*\). We prove that the roots of the Ehrhart polynomial of \(C_d^*\) have the same real part \(-1/2\), and we also prove that the Ehrhart polynomials of \(C_d^*\) for \(d=1,2,\ldots \) have the interlacing property.
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Acknowledgements
The authors would like to thank Masahiro Hachimori for a lot of his helpful comments on the results. The authors would also like to appreciate the numerous comments of the anonymous referees for the previous version of this paper. The first named author is partially supported by JSPS Grant-in-Aid for Scientists Research (C) 20K03513.
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Higashitani, A., Yamada, Y. The Distribution of Roots of Ehrhart Polynomials for the Dual of Root Polytopes of Type C. Graphs and Combinatorics 39, 83 (2023). https://doi.org/10.1007/s00373-023-02679-z
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DOI: https://doi.org/10.1007/s00373-023-02679-z