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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
250 Combinatorics of Permutations, Second Edition
RR
K
FIGURE 6.11
How corners cause non-cancelling terms.
PROOF We can express both f
F
and f
F
by the hooklength formula.
After that, m! cancels, and so do all hooklengths that belong to hooks not
being in the same row or column as
¯
K.
What happens with the remaining terms? Let
¯
K =(x, y). Looking at the
row of
¯
K, we see that the hook H
x,j
of F is as long as the hook H
x,j+1
of F
,
unless the vertical parts of these hooks are different, that is, unless there is a
corner R at the end of column j of F . In that case, instead of a cancellation, we
get a d(
¯
K,R)/d(
¯
K,
¯
R) factor. An analogous argument applies for the ...
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Publisher Resources

ISBN: 9781439850527