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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
Permutations and the Rest. Algebraic Combinatorics of Permutations. 305
38. Let ρ(n) be the size of the largest set of n-permutations in which every
pair of elements is colliding. Prove that ρ(n) ρ(n 1) + ρ(n 2).
39. Prove that for all positive integers n,wehaveS
n
(231, 312) = I
n
(231, 312).
Problems Plus
1. Let D
k
(n)bethenumberofn-permutations in which the longest in-
creasing subsequences have k elements and they all have at least one
element in common. Prove that D
k
(n)isaP -recursive function of n.
2. We have seen in Theorem 7.11 that the Robinson–Schensted–Knuth
correspondence naturally defines a bijection between inversions of length
n and SYT ...
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Publisher Resources

ISBN: 9781439850527