On Some Schützenberger Conjectures |
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Authors: | Clelia De Felice |
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Affiliation: | Dipartimento di Informatica ed Applicazioni, Università di Salerno, Baronissi, (SA), 84081, Italyf1 |
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Abstract: | In this paper we consider factorizing codes C over A, i.e., codes verifying the factorization conjecture by Schützenberger. Let n be the positive integer such that anC, we show how we can construct C starting with factorizing codes C′ with an′C′ and n′ < n, under the hypothesis that all words aizaj in C, with z(A\a)A*(A\a) (A\a), satisfy i, j, > n. The operation involved, already introduced by Anselmo, is also used to show that all maximal codes C=P(A−1)S+1 with P, SZA and P or S in Za can be constructed by means of this operation starting with prefix and suffix codes. Old conjectures by Schützenberger have been revised. |
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