2016/02/17 by Michel Deza, Deza, Michel, Mark Pankov +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics #Combinatorics (math.CO) #FOS: Mathematics #Mathematics #Rank (graph theory) #Topological and Geometric Data Analysis #math.CO
paper · pdf · doi:10.48550/arxiv.1602.05401
published in arXiv (Cornell University) (Cornell University) · The main result of the paper (Theorem 1) is a very simple consequence of the following trivial observation: the sum of the lengths of all zigzag is equal to the number of flags. So, it cannot be considered as a contribution
openalex publication_date 2016/02/17 · arxiv created 2016/03/29 · arxiv updated 2016/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider zigzags in thin complexes. The main result states that the sum of the lengths of all zigzags in an n-complexe is equal to the sum of the lengths of all zigzags in all (n-1)-faces of this complex, and this sum also is the twice of the sum of the lengths of all zigzags in all (n-2)-faces. For simplicial and cubical n-complexes, the sum depends on the rank n and the number of (n-1)-faces only. We also describe the sum of the lengths of all generalized zigzags, it depends on the rank and the number of flags. As an application, we find the number of zigzags in Coxeter complexes.