On Reverse-Free Codes and Permutations

  • Authors:
  • Zoltan Füredi;Ida Kantor;Angelo Monti;Blerina Sinaimeri

  • Affiliations:
  • furedi@renyi.hu;isvejda2@math.uiuc.edu;monti@di.uniroma1.it and sinaimeri@di.uniroma1.it;-

  • Venue:
  • SIAM Journal on Discrete Mathematics
  • Year:
  • 2010

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Abstract

A set $\mathcal{F}$ of ordered $k$-tuples of distinct elements of an $n$-set is pairwise reverse free if it does not contain two ordered $k$-tuples with the same pair of elements in the same pair of coordinates in reverse order. Let $F(n,k)$ be the maximum size of a pairwise reverse-free set. In this paper we focus on the case of 3-tuples and prove $\lim F(n,3)/\binom{n}{3}=5/4$, more exactly, $\frac{5}{24}n^3-\frac{1}{2}n^2-O(n\log n)