On some Schutzenberger conjectures

In this paper we consider factorizing codes C over A. i.e.. codes verifying the factorization conjecture by Schutzenberger. Let n be the positive inte ger such that a(n) is an element of C, we show how we can construct C start ing with factorizing codes C ' with a(n ' is an element of) C ' and n ' < n , under the hypothesis that all words a(i) za(j) in C. with z <is an elemen t of> (A\a)A*(A\a) boolean OR (A\a), satisfy i. j < n. The operation involv ed. already introduced by Anselmo. is also used to show that all maximal co des C = P(A - 1)S + 1 with P, S is an element of Z <A > and P or S in Z <a > can be constructed by means of this operation starting with prefix and su ffix codes. Old conjectures by Schutzenberger have been revised. (C) 2001 A cademic Press.