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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. 425
9. Theorem 7.5, with its notations, shows that necessarily a
1
= k and
a
1
+ a
2
+ ···+ a
r
= r · k. Thus necessarily a
1
= a
2
= ··· = a
r
= k
and a
r+1
<k, otherwise there would be r + 1 increasing subsequences of
length k that are disjoint. This means that the size of the last column
is m
k
= r. Applying (7.1) with k variables instead of k 1 and fixing
m
k
= r we get the proof exactly as we got the proof of Theorem 7.4.
11. In any SYT of shape F ,theentryn has to be in one of the inner corners.
So removing n from any such tableaux, we get an SYT of shape F
for
some F
that is part of the summation.
13. N
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Publisher Resources

ISBN: 9781439850527