Enumerating Pattern-avoiding Fishburn Permutations Subject to Seven Statistics

Abstract:

      Fishburn permutations are in bijection with several important combinatorial structures including interval orders. In this paper, we use the method of generating trees to enumerate two classes of pattern-avoiding Fishburn permutations subject to 7 classical statistics simultaneously. The classes of our interest are (321,312)-avoiding and (321,4123)-avoiding Fishburn permutations. The statistics of our interest are ascents, descents, inversions, right-to-left maxima, right-to-left minima, left-to-right maxima and left-to-right minima. Our results generalize a result by Egge.