8 2001 Opa (overseas Publishers Association) N.v. Morphisms Preserving Densities*
نویسندگان
چکیده
The notions of density, thinness, residue and ideal in a free monoid can all be expressed in terms of the infix order. Guided by these definitions we introduce the same notions with respect to arbitrary binary relations. We then investigate properties of these generalized notions and explore the connection to the theory of codes. We show that, under certain assumptions about the relation, density is preserved by an endomorphism or the inverse of an endomorphism if and only if-essentially-the endomorphism induces a permutation of the generators of the frc:e monoid.
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