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