Permutation Formula (thesis)

Abstract

Runs in permutations and similar topics have been studied by various authors under different names. Hegarty examined permutations of finite abelian groups which avoid what he called progressions. Riordan studied 3-runs (which he called 3-sequences) and derived a formula to compute the number of permutations containing x 3-runs with rise of 1 and a distance of 1. Dymacek investigated 3-runs with d = 1 and r = 1 or r = 2. To our knowledge there has not been a formula produced for the cases where both r > 1 and d > 1. [From Introduction]