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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
100 Combinatorics of Permutations, Second Edition
had to expand p
j+a
(resp. q
j+a
)intop
j+a+1
(resp. q
j+a+1
). At the end
of the procedure, we define Φ(p, q)=(q
n
,p
n
).
Example 3.23
Let n =6andk = 2, and let p = (125463), and q = (13)(24)(56). It is then
clear that j =4,andp
4
= (1243) and q
4
= (13)(24). After swapping, we
get the pair
(q
4
,p
4
) = ((13)(24), (1243)).
To make further computations easier, we note that p
5
= (12543) and
q
5
= (13)(24)(5).
The entry 5 would have to be inserted into the second gap position of p
4
to get p
5
, and into the fifth gap position of q
4
to get q
5
.Soweinsert5
into the second gap position of q
4
and in
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Publisher Resources

ISBN: 9781439850527