ABSTRACT
Codes play an important role in the study of the combinatorics on words. In this chapter, we discuss pcodes that play a role in the study of the combinatorics on partial words. While a code of words X does not allow two distinct decipherings of some word in X+, a pcode of partial words Y does not allow two distinct compatible decipherings in Y +. In Sections 8.1 to 8.6, the definitions and some important general properties of pcodes and the monoids they generate are presented. There, we describe various ways of defining and analyzing pcodes. In particular, many pcodes can be obtained as antichains with respect to certain partial orderings. We investigate in particular the Defect Theorem for partial words. In Section 8.7, we introduce the circular pcodes which take into account, in a natural way, the conjugacy operation that was discussed in Chapter 2. The main feature of these pcodes is that they define a unique factorization of partial words written on a circle. Throughout the chapter proofs will be sometimes omitted. They are left as exercises for the reader.
