DMS Combinatorics Seminar

Speaker: Zach Walsh  (Auburn University)

Title: Turán densities for matroid basis hypergraphs 

Abstract: An \((r, s, t)\)-daisy is an \(r\)-uniform hypergraph that adds a "stem" to the complete \(s\)-uniform \(t\)-vertex hypergraph. Ellis, Ivan, and Leader recently showed that the limit as \(r\) tends to infinity of the Turán densities of \((r, s, t)\)-daisies is positive, disproving a conjecture of Bollabás, Leader, and Malvenuto. This raises the following question: Precisely what is this limit? The hypergraphs constructed by Ellis, Ivan, and Leader are matroid basis hypergraphs, and we show that their construction is best-possible within the class of matroid basis hypergraphs.

This is joint work with Michael Wigal and Jorn van der Pol.