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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
152 Combinatorics of Permutations, Second Edition.
Note that the conjectured number c
n
q
is very small compared to the number
of all n-permutations, which is n!. In other words, this is a quite ambitious
conjecture.
The following conjecture may look even more ambitious, but that is a false
appearance.
CONJECTURE 4.9 [Stanley–Wilf conjecture, alternative version] Let
q be any pattern. Then the limit
L(q) = lim
n→∞
n
'
S
n
(q)
exists.
The first published proof of the fact that the above two versions of the
conjecture are equivalent is given in [12]. On one hand, it is obvious that
Conjecture 4.9 implies Conjecture 4.8. On the other hand, to prove the im-
plication ...
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Publisher Resources

ISBN: 9781439850527