Sunday, February 26, 2012

Local maxima in permutations

This post accompanies How many bumps?.

The CDF is the graphical illustration of the permutations of numbers to 1 to n (in this case illustrating 2,3,...,6). The average is calculated using a function that counts the local maxima in each permutation and then averages across all permutations. This quickly becomes unwieldy. The simplicity of the solution and the efficiency and beauty of the derivation provided by Professor Blitzstein is now self-evident.

It would have been nice to color the local maxima: perhaps another post.

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