Greedy balanced pairs in N-free ordered sets

Abstract An α -greedy balanced pair in an ordered set P = ( V , ≤ ) is a pair ( x , y ) of elements of V such that the proportion of greedy linear extensions of P that put x before y among all greedy linear extensions is in the real interval [ α , 1 − α ] . We prove that every N -free ordered set which is not totally ordered has a 1 2 -greedy balanced pair.