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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 Close. Permutations as Linear Orders. 43
44. (+) Keep the notation of the previous exercise, and let
C
n
(x)=
n
i=1
C
n,i
x
i
.
Prove that for all positive integers n, the roots of the polynomial C
n
(x)
are all real, distinct, and non-positive.
45. (–) Find a direct combinatorial proof (no generating functions, no al-
ternating runs) for the fact that for n 2, the number as(p) is even for
exactly half of all n-permutations p.
46. A permutation p = p
1
p
2
···p
n
is called a simsun permutation if there
exists no k n so that removing the entries larger than k from p,the
remaining permutation has two descents in consecutive positions. For
instance,
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Publisher Resources

ISBN: 9781439850527