On the supports of recognizable series over a field and a single letter alphabet

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).
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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⟩

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