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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 Anywhere. Permutations as Linear Orders. 73
PROOF As we have proved Theorem 2.17 by a bijection, this time we
present an inductive proof. Just as in the proof of Theorem 2.28, we first
treat the special case when K consists of a
1
copies of 1 and a
2
copies of 2
only, with a
1
+ a
2
= n. Denote this specific multiset by K
2
. In this special
case, the statement is obviously true for n = 1. Now let us assume that we
know the statement for all positive integers less than n, and prove it for n.
Now let us partition our permutations of K
2
according to the position of
the last 2. If the position of the last 2 is i, then we can be sure that there are
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Publisher Resources

ISBN: 9781439850527