On the deficit of a finite set of words

Abstract

We prove that the maximal independent sets of the free monoid A* are all the independent sets X satisfying |X|=|A|. However, for an independent set, being maximal is not equivalent to being a maximal code: take A={1,2}, X={12,21}; X is a maximal independent set but the set {12,21,11,22} contains X and is a (maximal) code. In fact, the only independent set which is a maximal code is the alphabet A