Zigzag structure of thin chamber complexes

2015/09/12 by Michel Deza, Deza, Michel, Mark Pankov +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1509.03754

arxiv created 2017/02/01 · arxiv updated 2017/02/02

Abstract

Zigzags and generalized zigzags in thin chamber complexes are investigated, in particular, all zigzags in the Coxeter complexes are described. Using this description, we show that the lengths of all generalized zigzags in the simplex α_n, the cross-polytope β_n, the 24-cell, the icosahedron and the 600-cell are equal to the Coxeter numbers of A_n, B_n=C_n, F₄ and H_i, i=3,4, respectively. Also, we discuss the following problem: in which cases two faces in a thin chamber complex can be connected by a zigzag?

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