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terrytao.wordpress.com | ||
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xenaproject.wordpress.com
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| | | | | (This is a guest post by Bhavik Mehta) On March 16, 2023, a paper by Campos, Griffiths, Morris, and Sahasrabudhe appeared on the arXiv, announcing an exponential improvement to the upper bound on Ramsey numbers, an open problem since 1935. Around the same time, posts by Terence Tao, Timothy Gowers and Gil Kalai appeared, all... | |
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lucatrevisan.wordpress.com
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| | | | | I am writing a short survey on connections between additive combinatorics and computer science for SIGACT News and I have been wondering about the "history" of the connections. (I will be writing as little as possible about history in the SIGACT article, because I don't have the time to research it carefully, but if readers... | |
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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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nhigham.com
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| | | A real $latex n\times n$ matrix $LATEX A$ is symmetric positive definite if it is symmetric ($LATEX A$ is equal to its transpose, $LATEX A^T$) and $latex x^T\!Ax > 0 \quad \mbox{for all nonzero vectors}~x. $ By making particular choices of $latex x$ in this definition we can derive the inequalities $latex \begin{alignedat}{2} a_{ii} &>0... | ||
