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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 Many Circles. Permutations as Products of Cycles. 135
(b) What can we say about the number of all n-permutations having
exactly one fixed point whose descent set is equal to {i}?
61. (+) Find a bijective proof of the equality SQ
2n
· (2n +1)=SQ
2n+1
.
62. Prove, without using generating functions, that SQ
2n+1
· (2n +2)
SQ
2n+2
.
63. Exercise 6 of Chapter 1 provided a probabilistic interpretation for the
Eulerian numbers. Why cannot we use that interpretation to deduce by
evy’s theorem (Theorem 3.37) that the Eulerian polynomials have real
roots only? Note that the Eulerian polynomials have irrational roots in
general, while the interpretation of the
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Publisher Resources

ISBN: 9781439850527