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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
162 Combinatorics of Permutations, Second Edition.
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FIGURE 4.2
A β(0, 1)-tree.
if v is an internal node and v
1
,v
2
, ···,v
k
are its children, then the in-
equality (v) 1+
k
i=1
(v
k
) holds. (This explains the number 1 in the
name of β(0, 1)-trees.)
Example 4.31
Figure 4.2 shows a β(0, 1)-tree on 12 vertices.
Let us call a permutation p = p
1
p
2
···p
n
indecomposable if there exists no
k [n 1] so that for all i k<j,wehavep
i
>p
j
.Inotherwords,p is
indecomposable if it cannot be cut into two parts so that everything before
the cut is larger than everything after the cut. For instance, 3142 is inde-
composable, but 43512 is not as we could choose ...
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Publisher Resources

ISBN: 9781439850527