2019/07/23 by Mathieu Dutour Sikirić, David A. Madore, David Madore +2 · 1 voice
Mathematics · #Advanced Combinatorial Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #math.CO
paper · pdf · doi:10.1112/jlms.12456
arxiv published 2019/07/23 · openalex created_date 2019/07/30 · arxiv updated 2021/03/22 · openalex publication_date 2021/05/03 · openalex updated_date 2026/08/04
In this paper we define the chromatic number of a lattice: It is the least number of colors one\nneeds to color the interiors of the cells of the Voronoi tessellation of a lattice so that no two cells\nsharing a facet are of the same color.\nWe compute the chromatic number of the root lattices, their duals, and of the Leech lattice,\nwe consider the chromatic number of lattices of Voronoi’s first kind, and we investigate the\nasymptotic behavior of the chromatic number of lattices when the dimension tends to infinity.\nWe introduce a spectral lower bound for the chromatic number of lattices in spirit of Hoffman’s\nbound for finite graphs. We compute this bound for the root lattices and relate it to the character\ntheory of the corresponding Lie groups.