Ekenta, Onyebuchi (Onye)
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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]
Thesis; [FULL-TEXT FREELY AVAILABLE ONLINE]Onyebuchi (Onye) Ekenta is a member of the Class of 2015 of Washington and Lee University.