기초과학연구원 이산수학그룹
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We present the KKM theorem and a recent proof method utilizing it that has proven to be very useful for problems in discrete geometry. For example, the method was used to show that for a planar family of convex sets with the property that every three sets are pierced by a line, there are three … |
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The Dedekind's Problem asks the number of monotone Boolean functions, a(n), on n variables. Equivalently, a(n) is the number of antichains in the n-dimensional Boolean lattice |
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Melchior’s Inequality (1941) implies that, in a rank-3 real-representable matroid, the average number of points in a line is less than three. This was extended to the complex-representable matroids by Hirzebruch in 1983 with the slightly weaker bound of four. In this talk, we discuss and sketch the proof of the recent result that, in … |
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For any finite point set |
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