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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 of pictures a
picture code which is the basis of the least DR-monoid
including .
A weak version of the defect theorem for pictures is established.
A characterization of picture codes through picture series is
also given.
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