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Arturo Merino, Torsten Mütze, and Namrata Apply Gliders for Hamiltonicty!
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Test Your Intuition (58): Polyhedra with 5-sided and 6-sided faces.
29 Jan 2025 |
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Let F be the class of planar 3-connected cubic graphs with n vertices, with all faces (including the outer face) are either pentagons or hexagons. Equivalently, F can be viewed as the family of graphs of simple 3-polytopes with n … Continue reading →
Annotated Pictures from Fall 2024
26 Jan 2025 |
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Apart from pictures, I write about the very first “Test your Intuition” question, a pioneering work of Tutubalin, the hierarchy of valuations of Lehman, Lehman, and Nisan, and three conjectures of Miki Tarsi. September 2024 Rothschild Symposium From left to … Continue reading →
Jiaoyang Huang, Theo Mckenzie, Horng-Tzer Yau: Ramanujan Property and Edge Universality of Random Regular Graphs
12 Jan 2025 |
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A central problem in combinatorics, probability theory, and analysis is to understand the spectrum of random d-regular graphs G with vertices. The following paper marks a huge leap in our understanding of this problem. Ramanujan Property and Edge Universality of … Continue reading →
The Answer to TYI (57): In Dimension Three or More, Intuitive Norms are Euclidean
10 Jan 2025 |
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Consider equipped with a norm. Given a finite set of points and a point , we consider , the sum of distances from to the points in . Next we consider the set of points that attain the minimum of … Continue reading →
Test Your Intuition (57): Are All Norms Nice?
7 Jan 2025 |
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Consider equipped with a norm. Given a finite set of points and a point , we consider , the sum of distances from to the points in . Next we consider the set of points that attain the minimum of … Continue reading →