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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
390 Combinatorics of Permutations, Second Edition
In other words, the set of n-permutations with k peaks consists of the
entire set of n-permutations with 2k + 1 alternating runs, half of the n-
permutations with 2k alternating runs, and half of the n-permutations
with 2k + 2 alternating runs. This proves
Peak(n, k)=G(n, 2k +1)+
G(n, 2k)+G(n, 2k +2)
2
.
35. It is easy to prove, by induction, or otherwise, that the number of de-
scents of p is equal to the number of right edges of T (p), while the
number of ascents of p is equal to the number of left edges of T (p). Now
it is clear that the symmetry of the sequence A(n, k)
k
can be proved by
the simple bijection ...
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Publisher Resources

ISBN: 9781439850527