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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
How Did We Get Here? Permutations as Genome Rearrangements. 361
(a) If P
a
and P
b
are part of the same alternating cycle C
ab
of G(p),
that is, when there is an alternating path A
da
from d to a ending in
a gray edge, then in G(p
), the cycle C
ab
will be replaced by three
cycles, namely the two-vertex cycles x 1 x and yy+1, andthe
cycle that contains b, d, the path A
da
,andc. Other cycles will not
change. See Figure 9.4 for an illustration.
x−1 a
yc
db
x y+1
x−1
d
y
x
b
ca
y+1
p
p’
FIGURE 9.4
The canonical block interchange of p when y and x are not adjacent, but are
part of the same cycle of G(p).
(b) If P
a
and P
b
are part of two distinct cycles C
a
and C
b
of G(p), then
in
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Publisher Resources

ISBN: 9781439850527