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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
182 Combinatorics of Permutations, Second Edition.
the best possible result. Josef Cibulka [90] has recently improved the upper
bound of Corollary 4.66 as follows. Let c
k
be the smallest constant satisfying
S
n
(q) <c
n
k
for all patterns q of length k, and all positive integers n.Then
there is a constant C so that the inequality
c
k
2
Ck log k
holds. Though this is a significant improvement, the upper bound obtained
for c
k
is still an exponential function of k.
The following definition enables us to discuss a conjecture that suggests a
much more realistic value for c
k
.
DEFINITION 4.67 A pattern q is called layered if q can be written as
the concatenation q
1
q
2
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Publisher Resources

ISBN: 9781439850527