A determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata
David Callan · Discrete Mathematics & Theoretical Computer Science · 2008
Combinatorics 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.