6 papers
Maximal matroids and counterexamples
Denys Bulavka, Martin Tancer
Jackson and Tanigawa conjectured that the rigidity matroid and the hyperconnectivity matroid are the unique maximal matroids in the posets of $\…
A short proof of the Hilton-Milner Theorem
Denys Bulavka, Russ Woodroofe
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
A Hilton-Milner theorem for exterior algebras
Denys Bulavka, Francesca Gandini, Russ Woodroofe
Recent work of Scott and Wilmer and of Woodroofe extends the ErdÅs-Ko-Rado theorem from set systems to subspaces of k-forms in an exterior algebra. We prove an extension of the Hi…
The typical algebraic shifting of a surface
Denys Bulavka, Eran Nevo, Yuval Peled
We initiate a statistical study of Kalai's exterior algebraic shifting, focusing on concentration phenomena for random triangulations of a fixed space. First, for a uniform -ver…
Computing shortest closed curves on non-orientable surfaces
Denys Bulavka, Ãric Colin de Verdière, Niloufar Fuladi
We initiate the study of computing shortest non-separating simple closed curves with some given topological properties on non-orientable surfaces. While, for orientable surfaces, a…
Strict ErdÅs-Ko-Rado theorems for simplicial complexes
Denys Bulavka, Russ Woodroofe
We show that if a simplicial complex is a near-cone of sufficiently high depth, then the only maximum families of small pairwise intersecting faces are those with a common intersec…