Discrete Mathematics & Theoretical Computer Science, Vol 10, No 2 (2008)

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A Determinant of Stirling Cycle Numbers Counts Unlabeled Acyclic Single-Source Automata

David Callan


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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