2014/12/30 by Djordje Baralić, Baralić, Djordje, Rade T. Živaljević +1
Computer Science · Mathematics · #14M25 #52B11 #54F45 #55M10 #55M30 #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #FOS: Mathematics #Metric Geometry (math.MG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1412.8621
openalex publication_date 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Following and developing ideas of R. Karasev (Covering dimension using toric varieties, arXiv:1307.3437), we extend the Lebesgue theorem (on covers of cubes) and the Knaster-Kuratowski-Mazurkiewicz theorem (on covers of simplices) to different classes of convex polytopes (colored in the sense of M. Joswig). We also show that the n-dimensional Hex theorem admits a generalization where the n-dimensional cube is replaced by a n-colorable simple polytope. The use of quasitoric manifolds offers great flexibility and versatility in applying the general method.