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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
Get Them All. Algorithms and Permutations. 323
THEOREM 8.18
For all fixed n and t, we have W
t
(n, k)=W
t
(n, n 1 k).
PROOF There seems to be no trivial reason for this symmetry. Indeed,
the usual symmetries of permutation classes (reverse, complement) that turn
ascents into descents do not preserve the t-stack sortable property, even when
t = 1. In order to prove our theorem, we need to find a more subtle symmetry
that turns ascents into descents, and preserves the t-stack sortable property
for any t.
Before we can define this symmetry, we need to extend the notion of binary
plane trees that we discussed in Exercise 27 of Chapter 4 in relation to 231-
av
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Publisher Resources

ISBN: 9781439850527