A determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata
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.
stirling cycle number sign-reversing involution unlabeled acyclic automaton column-marked subdiagonal path