MathDB

12

Part of 1990 IMO Longlists

Problems(1)

Find all real numbers c - ILL 1990 CZS5

Source:

9/19/2010
For any permutation pp of set {1,2,…,n}\{1, 2, \ldots, n\}, define d(p)=∣p(1)−1∣+∣p(2)−2∣+…+∣p(n)−n∣d(p) = |p(1) - 1| + |p(2) - 2| + \ldots + |p(n) - n|. Denoted by i(p)i(p) the number of integer pairs (i,j)(i, j) in permutation pp such that 1≦<j≤n1 \leqq < j \leq n and p(i)>p(j)p(i) > p(j). Find all the real numbers cc, such that the inequality i(p)≤c⋅d(p)i(p) \leq c \cdot d(p) holds for any positive integer nn and any permutation p.p.
inequalitiesalgebracombinatorial inequalitypermutationIMO ShortlistIMO Longlist