Enumerating cycles in the graph of overlapping permutations |
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Authors: | John Asplund N. Bradley Fox |
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Affiliation: | 1. Department of Technology and Mathematics, Dalton State College, Dalton, GA 30720, USA;2. Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, USA |
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Abstract: | The graph of overlapping permutations is a directed graph that is an analogue to the De Bruijn graph. It consists of vertices that are permutations of length and edges that are permutations of length in which an edge would connect the standardization of to the standardization of . We examine properties of this graph to determine where directed cycles can exist, to count the number of directed -cycles within the graph, and to enumerate the vertices that are contained within closed walks and directed cycles of more general lengths. |
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Keywords: | Overlapping permutations Cycles Closed walks |
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