An interlacing pattern between the types $C_n$ and $D_n$ coordinator polynomials

Jun-Ying Liu; Shi-Mei Ma

An interlacing pattern between the types $C_n$ and $D_n$ coordinator polynomials

Combinatorics 2026-08-11 v1

Authors: Jun-Ying Liu , Shi-Mei Ma

Abstract

The study of coordinator polynomials of Weyl group lattices was initiated by Conway and Sloane. In 2013, by using a trigonometric substitution approach, Wang and Zhao proved the real-rootedness of the type $D$ coordinator polynomials. Subsequently, Xie and Zhang proved the compatibility between the types $C_n$ and $D_n$ coordinator polynomials. In this paper, we discover the interlacing pattern between the types $C_n$ and $D_n$ coordinator polynomials, which may be named as the second pattern of interlacing zeros.

Keywords

coordinator polynomials Weyl group lattices interlacing pattern real-rootedness type C type D

Cite

@article{arxiv.2608.11012,
  title  = {An interlacing pattern between the types $C_n$ and $D_n$ coordinator polynomials},
  author = {Jun-Ying Liu and Shi-Mei Ma},
  journal= {arXiv preprint arXiv:2608.11012},
  year   = {2026}
}

Comments

6 pages