Combinatorics and Algebra Seminar-Shortening universal cycles for words, graphs, and permutations

Title: Shortening universal cycles for words, graphs, and permutations

Speaker: Rachel Kirsch, George Mason
Date and time: Friday, October 28, 4–5 pm
Place: Rome 204

Abstract: Universal cycles are cyclic sequences of symbols that represent every combinatorial object from some family exactly once as a consecutive subsequence. Universal partial cycles (or upcycles) are universal cycles for words (i.e., De Bruijn cycles) which have been shortened using a wildcard symbol. Introduced in 2016, upcycles appear to be much rarer than De Bruijn cycles, and were initially conjectured not to exist. In this talk I will present recent advances on constructions of upcycles, as well as on shortened forms of universal cycles for graphs and permutations.

This talk is on joint work with Dylan Fillmore, Bennet Goeckner, Corbin Groothuis, Cyrus Hettle, Brian Kell, Pamela Kirkpatrick, Bernard Lidický, Kirin Martin, Daniel McGinnis, Clare Sibley, Ryan Solava, and Elizabeth Sprangel, in various combinations.