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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
430 Combinatorics of Permutations, Second Edition
obtained from T (p) by omitting its labels. As there are C
n
such trees,
we get that B has C
n
=
2n
n
/(n +1)elements.
23. We have seen in Exercise 21 that going through a stack can effect an n-
permutationinatmostC
n
ways, so an n-permutation can have at most
C
n
preimages. On the other hand, the identity permutation does have
C
n
preimages, namely all the 231-avoiding permutations. We claim this
is the only permutation with that property.
To see that no other n-permutation can have C
n
preimages, we apply
induction on n.Forn 3, the statement is clearly true. Now let us
assume the statement is true for all positive integers less than n.If
s(q)=p,andq = LnR,thenwehavep = s(L)s(R)n. Now keep n fixed
in q, in positio ...
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Publisher Resources

ISBN: 9781439850527