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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
110 Combinatorics of Permutations, Second Edition
Thus the second cycle of p must start with the leftmost entry q
j
of q that
is larger than q
1
. By identical argument, the third cycle of q must start with
the leftmost entry of q larger than q
j
, and so on. The procedure will stop
with the cycle that starts with the entry n. This yields a deterministic, and
always executable, algorithm to find the unique preimage of q under p.
In our running example, we have q = 2417635. This yields q
1
=2. The
smallest j so that q
j
>q
1
is j = 2, so the second cycle will start in the second
position. Then, the leftmost entry larger than 4 is 7, so the third cycle starts
with ...
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Publisher Resources

ISBN: 9781439850527