ABSTRACT
A 0-1 matrix is said to be extendably $\tau$-avoiding if it can be the upper left corner of a $\tau$-avoiding permutation matrix. This concept arose in \cite{EL}, where the surprising result that the number of extendably 321-avoiding rectangles are enumerated by the ballot numbers was proved. Here we study the other five patterns of length three. The main result is that the six patterns of length three divides into only two cases, no easy symmetry can explain this. An other result is that the Simion-Schmidt-West-bijection for permutations avoiding patterns $12\tau$ and $21\tau$ works also for extended pattern avoidance. The results and proofs use many properties of the Catalan numbers and refinements of the Catalan numbers.