  The pattern-avoiding fillings of Young diagrams we study arose from
Postnikov's work on positive Grassman cells. They are called Le-diagrams, and
are in bijection with decorated permutations. Other closely-related diagrams
are interpreted as acyclic orientations of some bipartite graphs. The
definition of the diagrams is the same but the avoided patterns are different.
We give here bijections proving that the number of pattern-avoiding filling of
a Young diagram is the same, for these two different sets of patterns. The
result was obtained by Postnikov via a reccurence relation. This relation was
extended by Spiridonov to obtain more general results about other patterns and
other polyominoes than Young diagrams, and we show that our bijections also
extend to more general polyominoes.
