Abstract of Paper

Factorizing Codes and Schutzenberger Conjectures
by Clelia De Felice

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
Sch\"utzenberger. 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 $a^{n'}\in C'$ and $n'$ less than $n$, under the hypothesis that all
words $a^iwa^j$ in $C$, with $w^n bA^*b\cup\{b\}$, satisfy $i,j$ less than
$n$. The operation involved, already introduced by another author, is also
used to show that all maximal codes $C= P(A-1)S+1$ with $P,S\in Z\langle A\rangle$ and $P$ or $S$ in $Z\langle a\rangle$ can be constructed by means
of this operation starting from prefix and suffix codes. Inspired by
another early Sch\"utzenberger conjecture, we propose here an open problem
related to the results obtained and to the operation considered in this paper.