Seminar Details
Slow Fibonacci Walks
- Start Date: April 22, 2020
- Event Start Time: 1:00 PM
- Event End Time: 2:00 PM
- Seminar Series: Graduate Combinatorics Seminar
- Presenter(s): Sam Spiro - Georgia State University
- Event Location: Online Event
- Event Additional Info: <p><strong>SPECIAL NOTE: This seminar is presented online only.</strong></p> <p><strong>You can join via ZOOM with Meeting ID: 268 276 468 or by clicking this link <a href="https://nam02.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.google.com%2Furl%3Fq%3Dhttps%253A%252F%252Fbrown.zoom.us%252Fj%252F268276468%26sa%3DD%26sntz%3D1%26usg%3DAFQjCNFYXnnZZUuFfe2BnuubGw9k-0vxrQ&data=02%7C01%7Clindac%40dimacs.rutgers.edu%7C4ad593d020e04dbc204f08d7da3046bd%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C0%7C637217773197229520&sdata=At9drfT1SFLJTDjwBLaoJsIicKaiSAFC7YlyPWIMTJs%3D&reserved=0" target="_blank">https://brown.zoom.us/j/268276468</a></strong></p> <p>For further information see: <a href="https://sites.google.com/view/gocc-combinatorics/home">https://sites.google.com/view/gocc-combinatorics/home</a></p>
- Presentation Type: Stand Alone Presentation
- Abstract:
We define a Fibonacci walk to be any sequence of positive integers satisfying the recurrence w_{k+2} = w_{k+2} = w_{k+1}+w_k, and we say that a sequence is an n-Fibonacci walk if w_k = n for some k. Note that every $n$ has a number of boring n-Fibonacci walks, e.g. the sequence starting n, n, 2n, ... . To make things interesting, we consider n-Fibonacci walks which have w_k=n with k as large as possible, and we call this an n-slow Fibonacci walk. For example, the two 6-slow Fibonacci walks start 2, 2, 4, 6 and 4, 1, 5, 6. In this talk we discuss a number of properties about n-slow Fibonacci walks, such as the number of slow walks a given $n$ can have, as well as how many n have a given number of walks. We also discuss slow walks that follow other recurrence relations.
This is joint work with Fan Chung and Ron Graham.