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Number of cycles in the graph of $312$-avoiding permutations

Abstract : The graph of overlapping permutations is defined in a way analogous to the De Bruijn graph on strings of symbols. However, instead of requiring the tail of one permutation to equal the head of another for them to be connected by an edge, we require that the head and tail in question have their letters appear in the same order of size. We give a formula for the number of cycles of length $d$ in the subgraph of overlapping $312$-avoiding permutations. Using this we also give a refinement of the enumeration of $312$-avoiding affine permutations.
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Richard Ehrenborg, Sergey Kitaev, Einar Steingrımsson. Number of cycles in the graph of $312$-avoiding permutations. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.37-48. ⟨hal-01207587⟩

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