The Solution of a Conjecture of Stanley and Wilf for All Layered Patterns

Proving a conjecture of Wilf and Stanley in hitherto the most general case, we show that for any layered patternqthere is a constantcso thatqis avoided by less thancnpermutations of lengthn. This will imply the solution of this conjecture for at least 2kpatterns of lengthk, for anyk.