Crapo's beta invariant was defined by Henry Crapo in the 1960s. For a matroid $M$, the invariant $\beta(M)$ is the non-negative integer that is the coefficient of the $x$ term of the Tutte p...

Delta-matroids generalize matroids. In a delta-matroid, the counterparts of bases, which are called feasible sets, can have different sizes, but they satisfy a similar exchange property in which ...

A cube is a matroid over $C^n=\{-1,+1\}^n$ that contains as circuits the usual rectangles of the real affine cube packed in such a way that the usual facets and skew-facets are hyperplanes of the ...

The classical Tverberg's theorem says that a set with sufficiently many points in $R^d$ can always be partitioned into m parts so that the (m - 1)-simplex is the (nerve) intersection pattern of the ...