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One of those apt juxtapositions that Twitter occasionally throws up.pic.twitter.com/1g9z64wl0d
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This was posted to Math Overflow in 2018, but I just found it via a comment on
@Mathologer’s video https://www.youtube.com/watch?v=DjI1NICfjOk …, which also explains this proof.Prikaži ovu nit -
You know Zagier’s brilliant-but-baffling “one sentence proof” that every prime of the form 4k+1 is the sum of two squares? It turns out there’s a lovely intuitive explanation of it! https://mathoverflow.net/a/299696/8217 pic.twitter.com/uoSLHwjbF5
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Diagonal paths vs crenellated orthogonal paths:pic.twitter.com/WnKwIWnO53
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(It’s even simpler if we use crenellations rather than pyramids.)pic.twitter.com/jBHXIROcVe
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It occurs to me that your example has a simpler solution. I wonder how generalisable this is.pic.twitter.com/ShwMZWktuA
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I was quite wrong! That grid *is* a subset of an infinite grid with finitely many black cells. I wonder if all finite rectangular grids are.pic.twitter.com/HzHvyAnoiN
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But this grid can nevertheless be reduced to a white grid (assuming no special boundary conditions).pic.twitter.com/6J3xg0FfrI
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I suspect there are some finite grids, like this one, that are not a subset of any infinite grid with finitely many black cells.pic.twitter.com/7WZYAEDBdv
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I don’t think all the proofs were published, no. Zeilberger later reproved the Cosmological Theorem. https://www.ams.org/journals/era/1997-03-11/S1079-6762-97-00026-7/S1079-6762-97-00026-7.pdf …pic.twitter.com/jrnRIDuAlz
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Don’t miss the portrait of Georges Perec as a prime number. (Would Jacques Roubaud have been a more apt choice?)pic.twitter.com/SwvMf9NPmS
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If we have a node of the quotient graph, and an edge leading out of it, that determines a unique node of the original graph. Suppose not. Then we would have equivalent nodes (red and blue) connected by different edges.pic.twitter.com/JtMKf3qkTg
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and every N-shaped subgraph actually has the dotted edge too:pic.twitter.com/YL08WLYgVc
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As long as the graph has no subgraph like this, which I’ll call a diamond:pic.twitter.com/w0rik5kOwM
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Here (from Wikipedia) is a graph – showing the weight-1 edges only – for de Bruijn sequences with Σ = {0, 1} and s=3.pic.twitter.com/7fkHOYWgbe
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Here’s the graph for superpermutations with n=3, for example, where each edge is labelled with its weight. Weight-3 edges – such as 231→321 – are not shown.pic.twitter.com/ua1Kvav3NB
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