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Seminar Details

Entropy and Letter Density for Shifts of Finite Type

  • Start Date: April 17, 2023
  • Event Start Time: 2:00 PM
  • Event End Time: 3:00 PM
  • Seminar Series: Rutgers Discrete Mathematics Seminar
  • Presenter(s): Jacob Richey - University of British Columbia
  • Event Location: Conference Room 705 | Rutgers University | Hill Center | 110 Frelinghuysen Rd
  • Event Additional Info: <p>See:&nbsp;<a href="https://sites.google.com/view/rutgersdmseminar">https://sites.google.com/view/rutgersdmseminar</a></p>
  • Presentation Type: Stand Alone Presentation
  • 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.