## On de Bruijn Sequences with Varying Combs

- Oct. 19, 2015
- 3:30 p.m.
- LeConte 312

## Abstract

For a given alphabet A and length n, a de Bruijn sequence corresponds to a string of length |A|^n where every string of length n occurs as a consecutive substring (and we allow the ends to wrap around). In this talk, we present results of Alhakim, Butler, and Graham in which they allow the letters of the substring to occur in a pattern, called a comb. In particular, we present their construction for de Bruijn sequences of particular combs as well as their construction for combs that have no such cycle.