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Factorizing Codes and Schützenberger Conjectures

  • Clelia De Felice
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1893)

Abstract

In this paper we mainly deal with factorizing codes C over A, i.e., codes verifying the famous still open factorization conjecture formulated by Schützenberger. Suppose A = a,b and denote a n the power of a in C. We show how we can construct C starting with factorizing codes C∼ with a n ∈ C∼ and n < n, under the hypothesis that all words a i waj in C, with w ∈ bA*b ∪b, satisfy i; j<n. The operation involved, already introduced in [1], is also used to show that all maximal codes C = P(A - 1)S + 1 with P; S ∈ Z〈A〉 and P or S in Z〈a〉 can be constructed by means of this operation starting from prefix and sufix codes. Inspired by another early Schützenberger conjecture, we propose here an open problem related to the results obtained and to the operation introduced in [1] and considered in this paper.

Keywords

Characteristic Polynomial Discrete Math Unique Factorization Empty Word Free Monoid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Clelia De Felice
    • 1
  1. 1.Dipartimento di Informatica ed ApplicazioniUniversitá di SalernoBaronissi(SA)Italy

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