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A determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata

Abstract : We show that a determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata. The proof involves a bijection from these automata to certain marked lattice paths and a sign-reversing involution to evaluate the determinant. We also give a formula for the number of acyclic automata with a given set of sources.
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David Callan. A determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2008, Vol. 10 no. 2 (2), pp.77--86. ⟨10.46298/dmtcs.421⟩. ⟨hal-00972318⟩

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