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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 Any Way but This. Pattern Avoidance. The Basics. 187
37. Let f be the bijection defined in Exercise 17. Let B
m
be the set of
permutations in the domain of f that have exactly m inversions. Give
a simple description of f (B
m
).
38. Find three patterns p, q,andr so that for all positive integers n,we
have S
n
(p, q, r)=n.
39. Are there infinitely many nontrivial pairs of patterns p and q so that
S
n
(p, q) <h
(p,q)
(n) for all n,whereh
(p,q)
(n) is a polynomial function of
n? By nontrivial pairs we mean pairs in which at least one of the two
patterns has at least two alternating runs.
40. Find a formula for the number of 132-avoiding n-permutations whose
longest decreasing subsequence is of length exactly k +1.
41. Find a formula for the number B
1
(a
1
,a
2
,a
3
) of
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Publisher Resources

ISBN: 9781439850527