MathDB

2

Part of 1998 IMC

Problems(2)

composition of permutations

Source: IMC 1998 day 1 problem 2

11/1/2005
Consider the following statement: for any permutation π1≠I\pi_1\not=\mathbb{I} of {1,2,...,n}\{1,2,...,n\} there is a permutation π2\pi_2 such that any permutation on these numbers can be obtained by a finite compostion of π1\pi_1 and π2\pi_2. (a) Prove the statement for n=3n=3 and n=5n=5. (b) Disprove the statement for n=4n=4.
geometrygeometric transformationrotationsuperior algebrasuperior algebra unsolved
IMC 1998 Problem 8

Source: IMC 1998 Day 2 Problem 2

10/28/2020
SS ist the set of all cubic polynomials ff with ∣f(±1)∣≤1|f(\pm 1)| \leq 1 and ∣f(±12)∣≤1|f(\pm \frac{1}{2})| \leq 1. Find sup⁡f∈Smax⁡−1≤x≤1∣f′′(x)∣\sup_{f \in S} \max_{-1 \leq x \leq 1} |f''(x)| and all members of ff which give equality.
algebrapolynomialinequalities