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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
290 Combinatorics of Permutations, Second Edition
4 3 1
7 6 5 8 2
9
FIGURE 7.13
A balanced tableau.
out to be remarkably interesting. It was first answered by Richard Stanley
[238], who proved his own conjecture showing that the number of maximal
chains of P
n
is equal to the number of Standard Young Tableaux of shape
(n 1,n 2, ···, 2, 1). The proof in [238] uses symmetric functions, so the
quest for a combinatorial proof has continued. At this point, we mention
that a chain connecting permutation p to the identity permutation is called
a reduced decomposition of p, so the task at hand is finding the number of
reduced decompositions of n(n 1) ···21.
A
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Publisher Resources

ISBN: 9781439850527