Morphisms preserving densities

Abstract

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 free monoid.

Keywords:

• Codes-monoids
• Morphisms
• Density

C.R. Categories:

• F.4
• G.2

^*This research was supported by Grants OGP0000243, R28424A01 and OGP0007877 of the Natural Sciences and Engineering Research Council of Canada.

^† [email protected] [email protected]

^¶ [email protected]

^*This research was supported by Grants OGP0000243, R28424A01 and OGP0007877 of the Natural Sciences and Engineering Research Council of Canada.

^† [email protected] [email protected]

^¶ [email protected]

Notes

^*This research was supported by Grants OGP0000243, R28424A01 and OGP0007877 of the Natural Sciences and Engineering Research Council of Canada.

^† [email protected] [email protected]

^¶ [email protected]