a1 Department of Mathematics, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece; email@example.com; firstname.lastname@example.org
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.
(Received October 20 2003)
(Accepted June 15 2005)
(Online publication November 8 2006)
Mathematics Subject Classification: