2024 08 21 Matthew Kroeker Average Hyperplane Size In Complex Representable Matroids

Matthew Kroeker 2024 workshop on (mostly) matroidsmatthew kroeker, average hyperplane size in complex representable matroidsaugust 21, wednesday @ 1:30 pm 1:55 pm kstibs s. These results extend to complex representable and orientable matroids. finally, we formulate a high dimensional generalization of a classic problem of motzkin, grünbaum, erdős and purdy on sets of red and blue points in the plane with no monochromatic blue line.

Matthew Kroeker We show that, in every simple rank 4 real representable matroid which is not the direct sum of two lines, the average size of a plane is at most an absolute constant. we also present a generalization of this result to hyperplanes of arbitrary rank. this talk is based on joint work with rutger campbell, jim geelen and ben lund. Matthew kroeker postdoc, tu freiberg verified email at math.tu freiberg.de combinatorics. We show that the average plane size in a simple, rank $4$, complex representable matroid is bounded above by an absolute constant, unless the matroid is the direct sum of two lines. Generalizing a theorem of the first two authors and geelen for planes, we show that, for a real representable matroid $m$, either the average hyperplane size in $m$ is at most a constant depending only on its rank, or each hyperplane of $m$ contains one of a set of at most $r (m) 2$ lines.

Matthew Kroeker Gave A Talk On The Average Number Of Points On Affine We show that the average plane size in a simple, rank $4$, complex representable matroid is bounded above by an absolute constant, unless the matroid is the direct sum of two lines. Generalizing a theorem of the first two authors and geelen for planes, we show that, for a real representable matroid $m$, either the average hyperplane size in $m$ is at most a constant depending only on its rank, or each hyperplane of $m$ contains one of a set of at most $r (m) 2$ lines. Thew e. kroeker, and ben lund abstract. generalizing a theorem of the first two authors and geelen for planes, we show that, for a real representable matroid m, either the average hyperplane size in m is at most a constant depending only on its rank, or each hyperplane of m contains o. We show that the average plane size in a simple, rank 4, complex representable matroid is bounded above by an absolute constant, unless the matroid is the direct sum of two lines. Rutger campbell, matthew e. kroeker, and ben lund, characterizing real representable matroids with large average hyperplane size, 2024. Theorem 1.1. in a simple complex representable matroid m with rank at least 4, the average plane size is bounded above by an absolute con stant, unless m is the direct sum of two lines.

Matthew Kroeker Industrial Designers Society Of America Thew e. kroeker, and ben lund abstract. generalizing a theorem of the first two authors and geelen for planes, we show that, for a real representable matroid m, either the average hyperplane size in m is at most a constant depending only on its rank, or each hyperplane of m contains o. We show that the average plane size in a simple, rank 4, complex representable matroid is bounded above by an absolute constant, unless the matroid is the direct sum of two lines. Rutger campbell, matthew e. kroeker, and ben lund, characterizing real representable matroids with large average hyperplane size, 2024. Theorem 1.1. in a simple complex representable matroid m with rank at least 4, the average plane size is bounded above by an absolute con stant, unless m is the direct sum of two lines.

Matthew Kroeker Regional Business Development Officer In Aurora Co Rutger campbell, matthew e. kroeker, and ben lund, characterizing real representable matroids with large average hyperplane size, 2024. Theorem 1.1. in a simple complex representable matroid m with rank at least 4, the average plane size is bounded above by an absolute con stant, unless m is the direct sum of two lines.

Matthew Kroeker Regional Business Development Officer In Aurora Co