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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
In One Line and Anywhere. Permutations as Linear Orders. 63
the major index or greater index maj(p) of p to be the sum of the descents of
p. That is, maj(p)=
iD(p)
i.
Example 2.16
If p = 352461, then D(p)={2, 5}, therefore maj(p)=7.
In 1916, MacMahon showed [201] the following surprising theorem by prov-
ing that the two relevant generating functions were identical. It was not until
1968 that a bijective proof was found by Dominique Foata [129], who worked
in a more general setup. Another proof that can be turned into a bijective
proof is given in Exercises 31 and 32. We present Foata’s proof in the simpli-
fied language of permutations.
THEOREM 2.17
F
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Publisher Resources

ISBN: 9781439850527