The 15 puzzle problem

Abstract: An $n^2-1$ puzzle is a children's toy with $n^2-1$ numbered pieces on an $n \times n$ grid, with one missing piece. A move in the puzzle consists of sliding an adjacent numbered piece into the location of the missing piece. I will discuss joint work with Yang Chu which studies the asymptotic mixing of an $n^2-1$ puzzle when random moves are made. The techniques involve characteristic function methods for studying the renewal process described by the sequence of moves of one or several pieces.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2021)

Series comments: This is the nineteenth in a series of annual workshops sponsored by the New York Number Theory Seminar on problems in combinatorial and additive number theory and related parts of mathematics.

Registration for the conference is free. Register at cant2021.eventbrite.com.

The conference website is www.theoryofnumbers.com/cant/ Lectures will be broadcast on Zoom. The Zoom login will be emailed daily to everyone who has registered on eventbrite. To join the meeting, you may need to download the free software from www.zoom.us.

The conference program, list of speakers, and abstracts are posted on the external website.