2007/09/30 by Taoyang Wu, Wu, Taoyang
Computer Science · Engineering · #05C20 #05C85 #68R05 #68W01 #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0710.0125
openalex publication_date 2007/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Configurations are necklaces with prescribed numbers of red and black beads. Among all possible configurations, the regular one plays an important role in many applications. In this paper, several aspects of regular configurations are discussed, including construction, uniqueness, symmetry group and the link with balanced words. Another model of configurations is the polygons formed by a given number of sides of two different lengths. In this context, regular configurations are used to obtain a lower bound for the cycles packing number of shift graphs, a subclass of the directed circulant graphs.