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Combinatorics of Permutations, 2nd Edition
book

Combinatorics of Permutations, 2nd Edition

by Miklos Bona
April 2016
Intermediate to advanced content levelIntermediate to advanced
478 pages
14h 44m
English
Chapman and Hall/CRC
Content preview from Combinatorics of Permutations, 2nd Edition
In One Line and Close. Permutations as Linear Orders. 13
objects. Take a permutation p counted by A(n, k). The k ascending runs of
p then naturally define an ordered partition of [n]intok parts. If k = r,then
there is nothing left to do. If k<r, then we will split up some of the ascending
runs into several blocks of consecutive elements, in order to get an ordered
partition of r blocks. As we currently have k blocks, we have to increase the
number of blocks by r k. This can be achieved by choosing r k of the
n k “gap positions” (gaps between two consecutive entries within the same
block).
This shows that we can generate
r
k=0
A(n, k)
nk
rk
ordered ...
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Publisher Resources

ISBN: 9781439850527