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www.jeremykun.com | ||
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jeremykun.wordpress.com
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| | | | | Define the Ramsey number $ R(k,m)$ to be the minimum number $ n$ of vertices required of the complete graph $ K_n$ so that for any two-coloring (red, blue) of the edges of $ K_n$ one of two things will happen: There is a red $ k$-clique; that is, a complete subgraph of $ k$... | |
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gowers.wordpress.com
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| | | | | Here is a simple but important fact about bipartite graphs. Let $latex G$ be a bipartite graph with (finite) vertex sets $latex X$ and $latex Y$ and edge density $latex \alpha$ (meaning that the number of edges is $latex \alpha |X||Y|$). Now choose $latex (x_1,x_2)$ uniformly at random from $latex X^2$ and $latex (y_1,y_2)$ uniformly | |
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algorithmsoup.wordpress.com
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| | | | | The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... | |
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blog.demofox.org
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| | | This post explains how to use sliced optimal transport to make blue noise point sets. The plain, well commented C++ code that goes along with this post, which made the point sets and diagrams, is at https://github.com/Atrix256/SOTPointSets. This is an implementation and investigation of "Sliced Optimal Transport Sampling" by Paulin et al (http://www.geometry.caltech.edu/pubs/PBCIW+20.pdf).?They also have... | ||
