Abstract : We prove that the support of a recognizable series over a field of characteristic zero and a single letter alphabet is recognizable. This provides an answer to a question of Kirsten (2009). Then we give an example of a recognizable series over a field of prime characteristic and a single letter alphabet whose support is not recognizable which provides an answer to a question of Kirsten and Quaas (2011).
https://hal-univ-paris.archives-ouvertes.fr/hal-00663147
Contributor : Ines Klimann <>
Submitted on : Thursday, January 26, 2012 - 10:50:14 AM Last modification on : Thursday, October 1, 2020 - 9:33:13 AM Long-term archiving on: : Friday, April 27, 2012 - 2:35:03 AM
Guillaume Chapuy, Ines Klimann. On the supports of recognizable series over a field and a single letter alphabet. Information Processing Letters, Elsevier, 2011, 111 (23-24), pp.1096-1098. ⟨10.1016/j.ipl.2011.09.010⟩. ⟨hal-00663147⟩