@MISC{Radhakrishnan01anote, author = {Jaikumar Radhakrishnan}, title = {A Note on Scrambling Permutations}, year = {2001} }

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Abstract

A family F of permutations of [n] is completely k-scrambling [7] if for every sequence hp 1 ; p 2 ; : : : ; p k i of k distinct elements of [n], there is a permutation 2 F with (p 1 ) < (p 2 ) < < (p k ): We show that the size of the smallest completely k-scrambling family of permutations of [n] is at least 1 + 2 log 2 e n 2n k + 1 (k 1)! log 2 (n k + 2): This improves the previous best lower bound, due to Furedi [2], by a factor of approximately 2= log 2 e.