2018/09/24 by Zeying Xu, Xu, Zeying
Computer Science · Mathematics · #52B05 #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #math.CO #msc:52B05
paper · pdf · doi:10.48550/arxiv.1809.08764
10 pages
arxiv created 2018/09/24 · openalex publication_date 2018/09/24 · arxiv updated 2018/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We are interested in constructing zonotopes which are combinatorially nonequivalent but have the same face vector. In this paper we introduce a quadrilateral flip operation on graphs. We show that, if one graph is obtained from another graph by a flip, then the face vectors of the graphical zonotopes of these two graphs are the same. In this way, we can easily construct a class of combinatorially nonequivalent graphical zonotopes which share the same face vector. It is known that all triangulations of the n-gon are connected through the flip operation. Thus their graphical zonotopes have the same face vector. We will compute this vector and the total number of faces.