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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
192 Combinatorics of Permutations, Second Edition.
Solutions to Problems Plus
1. First, note that in a 132-avoiding permutation, the entry p
i
is a left-
to-right minimum if and only if either i =1,ori 1 is a descent.
Therefore, we are looking for the number of 132-avoiding n-permutations
with k descents, or, by taking the reverse, 231-avoiding n-permutations
with k ascents. We know from Exercise 17 that the number of such n-
permutations is equal to the number of northeastern lattice paths from
(0, 0) to (n, n)thathavek north-to-east turns and that never go above
the main diagonal. A comprehensive survey of lattice paths of this and
more general kinds ...
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Publisher Resources

ISBN: 9781439850527