https://hal.inria.fr/hal-00972318Callan, DavidDavidCallanDepartment of Statistics [Madison] - University of Wisconsin-MadisonA determinant of Stirling cycle numbers counts unlabeled acyclic single-source automataHAL CCSD2008[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Inria Sophia Antipolis-MÃ©diterranÃ©e / I3s, Service Ist2014-04-03 16:10:232019-04-04 11:30:042014-04-03 16:37:49enJournal articleshttps://hal.inria.fr/hal-00972318/document10.46298/dmtcs.421application/pdf1We 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.