Abstract
Two partial orders that play an important role in the combinatorics of words, can be defined in a natural way on the free monoid X* generated by the finite alphabet X: the infix and the embedding orders. A set C of nonempty words is called an infix code (hypercode) over X if C is an antichain with respect to the infix (embedding) order. A set of words is said to be e-convex if it is convex with respect to the embedding order. Two characterizations of the e-convex infix codes are given as well as a sufficient condition for such codes to be finite. It is shown that the family EIC(X) of the e-convex infix codes with the empty word forms, under the operation of concatenation, a free submonoid of the free monoid B(X) of the biprefix codes and that the generating alphabet of EIC(X) is a sub-alphabet of the generating alphabet of B(X).
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