Department of Mathematics,
Aristotle University of Thessaloniki,
54006 Thessaloniki, Greece;
Accepted: 15 June 2005
We introduce doubly-ranked (DR) monoids in order to study picture codes. We show that a DR-monoid is free iff it is pictorially stable. This allows us to associate with a set C of pictures a picture code B(C) which is the basis of the least DR-monoid including C. A weak version of the defect theorem for pictures is established. A characterization of picture codes through picture series is also given.
Mathematics Subject Classification: 94B60
Key words: Picture codes / picture series.
© EDP Sciences, 2006