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Post ARL51i4zkWDMIubl0i by [email protected] |
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Post #ARL51f98eekLCtWWYK by [email protected] |
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If you don't know what this is about start reading a summary by @johncarlos… |
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Post #ARL51ftDtJbrVp5KNs by [email protected] |
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The vertices of the horizontal graph are the horizontal line segments of the re… |
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Post #ARL51gJ6L6JGo5Bzii by [email protected] |
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Now pick an orientation of the rectangles (i.e. specify if they are short and w… |
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Post #ARL51h1PgLkt1VvNmy by [email protected] |
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We will distinguish between the 'outer vertices' (the ones labeled NESW… |
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Post #ARL51hdhO0NcwFpxSq by [email protected] |
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Similarly for the vertical graph we get the relations\[\sum_{r_i \in in(v)} v_i… |
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Post #ARL51i4zkWDMIubl0i by [email protected] |
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Now you can see that if all the above relations are satisfied we actually get a… |
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Post #ARL51ibbnGInw3rnqS by [email protected] |
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In our example if we orient \(r_1 = A -> V, r_2 = B -> H, r_3 = C -> V… |
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Post #ARL51jT8aF7Wc4uYHQ by [email protected] |
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Lemma: Let \(N\) be the number of rectangles in the rectangulation. There are \… |
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Post #ARL51kFLgzgX1bT3QW by [email protected] |
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This way we removed exactly 1 rectangle and one equation (line segment). If the… |
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Post #ARL51kilvbDkUrEYHw by [email protected] |
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This means we have a system of \(N+1\) equations with \(N+1\) variables. So we … |
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Post #ARL51lEg0yk25oA21A by [email protected] |
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The polynomial we obtain cannot be the zero polynomial, since this would imply … |
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Post #ARL5bTsy02UQhu2TCK by [email protected] |
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@Lisanne wrote: "For each internal vertex of the horizontal graph we have … |
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Post #ARLKUgEJCjNaHGEj5c by [email protected] |
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@Lisanne @johncarlosbaez hey, are you guys looking, i bet there are some curiou… |
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Post #ARLKUgJcsxdIXkiyNU by [email protected] |
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@barrygoldman1 - there are lots of things to say about this. You can take a go… |
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Post #ARNJyEZt1u2mpJHQDg by [email protected] |
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@johncarlosbaez @Lisanne Also the equation\[ \sum_{r_i\in\text{in}(v)} v_i a_i … |
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Post #ARNKFm6lcNDnk41Wsq by [email protected] |
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@deinst @Lisanne - there's a really cool current/voltage, series/parallel, … |
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Post #ARNwMDkXYaXdSy7zeK by [email protected] |
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@johncarlosbaez @Lisanne Start with a horizontal graph. By construction this is… |
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Post #ARObzWlWsztVrES5x2 by [email protected] |
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@johncarlosbaez @deinstI think I understand the current analogy! The faces of t… |
