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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
Do Not Look Just Yet. Solutions to Odd-Numbered Exercises. 415
Solutions for Chapter 5
1. We claim that S
132,1
(n)=
2n3
n3
. See [42] for a proof. The main idea is
the following. In a permutation enumerated by S
132,1
(n), there is either
one or no front entry that is smaller than a back entry. If there is one
such front entry, then its position and size is very restricted. If there is
no such front entry, then the single 132-pattern of the permutation is
formed either by front entries only, or by back entries only. This leads
to a recursive formula involving the numbers S
132,1
(n) and the Cata-
lan numbers, and solving that recursion, we obtain the a
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Publisher Resources

ISBN: 9781439850527