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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
2
In One Line and Anywhere. Permutations as
Linear Orders. Inversions.
2.1 Inversions
2.1.1 The Generating Function of Permutations by Inver-
sions
In Section 1.3, we looked at descents of permutations. That is, we studied
instances in which an entry in a permutation was larger than the entry directly
following it. A more comprehensive permutation statistic is that of inversions.
This statistic will look for instances in which an entry of a permutation is
smaller than some entry following it (not necessarily directly).
DEFINITION 2.1 Let p = p
1
p
2
···p
n
be a permutation. We say that
(p
i
,p
j
) is an inversion of p if i<j but p
i
>p
j
.
Example 2.2
Permutation 31524 ...
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Publisher Resources

ISBN: 9781439850527