Permutation Patterns for RealValued Functions
MSRIUP 2013: Algebraic Combinatorics June 15, 2013  July 28, 2013
Location: SLMath: Eisenbud Auditorium
v1099
Consider the sequence [x,f(x),f(f(x))=f2(x),…,fn−1(x)] where f is a realvalued function and n≥2. We can associate a permutation to every such sequence by comparing it with x1<x2<...<xn, where xi=fj−1(x) for some j=1,2,…,n. Permutations that arise from these sequences are called allowed permutations and those that do not are called forbidden permutations.For example, the logistic map, f:[0,1]→[0,1] is defined by f(x)=rx(1−x) where 0≤r≤4, for any x. We focus on enumerating the number of forbidden permutations for the logistic map and other functions, including trigonometric functions. For example, for the n=3 case, we have found that the oneline permutation (321) is a forbidden permutation for the function sin(πx).
v1099
H.264 Video 
v1099.m4v

Download 
Quicktime 
v1099.mov

Download 
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.