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Enumerating cycles in the graph of overlapping permutations. (English) Zbl 1376.05070
Summary: 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 $$n$$ and edges that are permutations of length $$n+1$$ in which an edge $$a_1 \cdots a_{n+1}$$ would connect the standardization of $$a_1 \cdots a_n$$ to the standardization of $$a_2\cdots a_{n+1}$$. We examine properties of this graph to determine where directed cycles can exist, to count the number of directed 2-cycles within the graph, and to enumerate the vertices that are contained within closed walks and directed cycles of more general lengths.

##### MSC:
 05C30 Enumeration in graph theory 05C38 Paths and cycles 05C20 Directed graphs (digraphs), tournaments
##### Keywords:
overlapping permutations; cycles; closed walks
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##### References:
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