Log-concavity, the Ulam distance and involutions

2015/02/18 by Miklós Bóna, Bóna, Miklós, Marie-Louise Bruner +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1502.05438

17 pages

arxiv created 2015/02/18 · arxiv updated 2015/02/20

Abstract

We prove that in a large collection of naturally defined sets of permutations of fixed length, the numbers of permutations at Ulam distance k from the identity form a log-concave sequence in k.

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