Jacob Richey, University of British Columbia

Abstract

Given an iid binary string conditioned to not have 1001 as a substring, how many 1s and 0s does it typically have? More generally, given a finite set of 'forbidden' patterns over a finite alphabet, we can study the associated shift of finite type, i.e. all strings avoiding the forbidden set. Which forbidden sets are the most/least restrictive, and which give a higher/lower density of 1s? I will present old and new results, and many unanswered questions. Combinatorics, probability, and symbolic dynamics will each play a role.

See: https://sites.google.com/view/rutgersdmseminar