Shuffle Relations and Codes

Abstract

Abstract An infinite hierarchy of reflexive and antisymmetric binary relations is defined on X. These relations, called the n-shuffle relations, include the embedding order and are included in the infix order. They are not transitive except for n= 1 and their transitive closure is the embedding order. The corresponding antichains form a family of codes called the n-shuffle codes and these families of codes form an infinite hierarchy of submonoids of the free monoid of prefix codes. Some characterizations of n-shuffle codes are investigated as well as the properties of their syntactic monoids.