A combinatorial proof of the log-concavity of the number of permutations with $k$ runs

Miklos Bona

University of Florida

February 11,
refreshments at 3:45pm


We combinatorially prove that the number $R(n,k)$ of permutations of length $n$ having $k$ runs is a log-concave sequence in $k$, for all $n$. Our proof involves a simple and useful lattice path interpretation of permutations. We also give a new combinatorial proof for the log-concavity of the Eulerian numbers. This is joint work with Richard Ehrenborg.

Speaker's Contact Info: bona(at-sign)math.ufl.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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