2026-04-29T14:27:09Z https://yabu.me Joshua Grochow https://yabu.me/npub1nf0sjfdvmx76z2dy28d6ky8kfnypfj5ey79uvflh6dm20egszsns0ng3kl https://media.mathstodon.xyz/accounts/avatars/000/287/987/original/6264c9ec054fb54e.jpg https://media.mathstodon.xyz/accounts/avatars/000/287/987/original/6264c9ec054fb54e.jpg https://yabu.me/nevent1qqswn48q3nhzz2n8x9g236wgpf33s6a7hsc76q9celh99xlz90dw9wczyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zwxz9s74 In reply to <a href='/nevent1qqs8q36pah0aj989mxrlxqzww52evz68vc2n8zcqr3s4qe4dg5supaq0tchjl'>nevent1q…chjl</a><br/>_________________________<br/><br/>Even in the noncommutative case, it is not known that 23 is the best you can do, it&#39;s just that 23 is the best known to date! I believe the best known lower bound is still only 19 (due to Bläser; though I vaguely recall this was improved to 20 at some point but I can&#39;t find that at the moment.) 2026-01-01T22:27:20Z https://yabu.me/nevent1qqsxzmse29ef3a00qa860930p9a23ys3z7yexc5te59frwsyr3p9a7szyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zw8kjkzx In reply to <a href='/nevent1qqsr0cdght5l34mny2qhuaky7sv7a29n2p3lv2cpadr3kcgn6qy6asqwmhulx'>nevent1q…hulx</a><br/>_________________________<br/><br/>I mean, r^4 is central, and acts as -1 in those irreps, so the 8 points of that G-set arise as a generic orbit in the projective space of either of the faithful 2D irreps. (cc <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1whrara5n38jvwcnkhwz346nl2sn969zu0guk0pvfeltzecn2axesdzqc2t" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>julesh</span> (<span class="italic">npub1whr…qc2t</span>)</a></span>) 2025-03-27T03:13:59Z https://yabu.me/nevent1qqsym8jrfeg5t646gty0nw4k5r378phh7md8a3c9rwfqpeprc7xv83gzyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zwhruuzk In reply to <a href='/nevent1qqsz3ppyzmkddtp5wzhq48h3gl6cgdzf6hn23wl57y0mz9sx0utg8vq6x3vf6'>nevent1q…3vf6</a><br/>_________________________<br/><br/>I was hoping to see it in a vector space so the &#34;geometry&#34; of the &#34;figure&#34; would be obvious. Notice that r^4 also generates an order 2 subgroup that&#39;s not conjugate to s, so that&#39;s a different 8-point G-set 2025-03-27T01:30:14Z https://yabu.me/nevent1qqswup9prntp6zv75ea8zsf7yhqwugmeg7chr2p2vsscnmvpqcmagmqzyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zw0c65yq In reply to <a href='/nevent1qqsyt2cul8g98735dkq5t8p4ka42jadedm9hge0rjqnkxyxa4lwxp0shqma8f'>nevent1q…ma8f</a><br/>_________________________<br/><br/>it&#39;s got two (Galois-conjugate) faithful 2D irreps over C:<a href="https://people.maths.bris.ac.uk/~matyd/GroupNames/1/SD16.html">https://people.maths.bris.ac.uk/~matyd/GroupNames/1/SD16.html</a>. A generic orbit there contains 16 points, so will give you a shape, but I have no idea what it is.<br/><br/>A subgroup of order 2 acts as -I on those reps, so each orbit consists of 8 points and their antipodes.<br/><br/>The reps seem to genuinely be complex (bc the characters include sqrt(-2)), so you probably really have to think of it as 16 points in C^2, which might be harder to visualize than R^2. 2025-03-25T18:43:40Z https://yabu.me/nevent1qqsxqpwrvys3l9rm0hkexcv9ld9n8ttqfxfyv3jnjd8mxhj69tw4a5czyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zwz5a2y2 In reply to <a href='/nevent1qqsggzzx5k356c3y550jdpy9r57senz6weltc3cnllhf2f744v7gygshg3nnk'>nevent1q…3nnk</a><br/>_________________________<br/><br/>oh, uh, maybe not. Just explains why derivations appeared when computing automorphism of GA(1,Z/8).<br/><br/>But the three types of edges I do have some sort of an explanation for.<br/><br/>Think of B=Z/8=red vertices as the base. The blue vertices and edges between them are something like a global section of a certain 6-fold etale cover of the graph B w edges=odd differences. <br/><br/>Between red verts (in B) there are 3 natural choices for edge set (these are the orbitals of GA(1,Z/8)): nearby, opposite, and distant in <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub12cuzzqzv8e8y7na77a9zv47mx2v6pec60qs5h7takzmv5p0mw0fsmgd38p" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Greg Egan</span> (<span class="italic">npub12cu…d38p</span>)</a></span>&#39;s terminology. Since the edges btwn blue verts cover the distant edges, we should really include nearby edges in B with one color and opposite with another. To make McGee 3-regular, choose to make opposite pairs edges and nearby pairs non-edges in B.<br/><br/>The edges between blue and red vertices are then just the 2-fold &#34;covering map&#34; (it&#39;s not quite a cover, because it&#39;s 2-to-1 but over each odd edge that would be present in the base there&#39;s only one blue edge instead of 2). 2025-03-18T19:29:14Z https://yabu.me/nevent1qqspdxdwwzsgnckarg8uulmvlvprf4pa8dk6zgs9du5wy9zqw8gjpfczyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zwllc2gl In reply to <a href='/nevent1qqs0w4tq96kfjxe5k003qmsm8cmzpvzkwydx4pwf9wc4a7lj33qsr7cuvttq4'>nevent1q…ttq4</a><br/>_________________________<br/><br/>This totally nerd-sniped me.<br/><br/>For the role of derivations in automorphisms of group extensions, check out the Wells exact sequence (and more recent work on it e.g. Buckley, Malfait, Jin-Liu), nicely exposited (w/ refs) by Jill Dietz in <a href="https://doi.org/10.1017/CBO9781316227343.013">https://doi.org/10.1017/CBO9781316227343.013</a>. <br/><br/>I had some thoughts about building the McGee graph from covering graphs (or etale covers, at least), but I think maybe they are too complicated to be worth writing down. 2025-03-18T18:53:45Z https://yabu.me/nevent1qqs0w4tq96kfjxe5k003qmsm8cmzpvzkwydx4pwf9wc4a7lj33qsr7czyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zwhadaze In reply to <a href='/nevent1qqs8myk57fj7ekq4ar5fwm84759u0eu4v2cj8d7fwrh8yy4ur834prqjnq2yg'>nevent1q…q2yg</a><br/>_________________________<br/><br/>Oh, I don&#39;t think you were arguing against what I was saying at all - sorry if I phrased something that way. Just trying to figure out where the cohomology is here! 2025-03-18T01:09:13Z https://yabu.me/nevent1qqs2jlkt20x4qpdwu4f6uxz3t2550uqh6s6jnj7tcp59mz0fupyvzeszyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zwxghmlc In reply to <a href='/nevent1qqsyzn8mhaj2g6v4esscnqan8jqaezw3g00hav2t06pt23t3rfy3hssqxf07p'>nevent1q…f07p</a><br/>_________________________<br/><br/>I mean, sure, but I feel like that fits in the following analogy<br/><br/>cohomology class : automorphism coming from a crossed hom<br/>::<br/>nontrivial coho class : non-inner automorphism coming from a crossed hom<br/><br/>And then the thing about class-preserving is a subgroup of automorphisms coming from crossed homs 2025-03-17T23:43:55Z https://yabu.me/nevent1qqszqe5ltzmsc53sqguse3gs4mekrrftqcn4nlq7yuld84sl099p56szyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zwkvargx In reply to <a href='/nevent1qqs06mzp2yen4h3480mh60550zsxqelr93zzdrt3djdjzghr200eeagg648y4'>nevent1q…48y4</a><br/>_________________________<br/><br/>the gif in the first post looks very Mobius-y. Looks like you can view the graph in terms of a 3-cover of the 8-cycle, where you then connect the 3 vertices in each fiber in a path (blue-red-blue) and then add in the red edges after. Definitely feels like something cohomology-y going on.<br/><br/>(But I should be doing other things now - maybe I&#39;ll give a shot at making this more precise in a day or two.) 2025-03-17T06:02:14Z https://yabu.me/nevent1qqsf40ylfaes9sgh2qf3rrhg0ljfwqfd0x5gwe0skq3tjc865uhnxtczyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zwzps0ha In reply to <a href='/nevent1qqswr667jhut7qs6jeucpkftmunqc9zhjzpmlmc4agcmxql68pk9vkgp0lw2z'>nevent1q…lw2z</a><br/>_________________________<br/><br/>those equations are exactly the definition of crossed homomorphism in this context (they all follow from the first equation, using the fact that the group doing the acting is commutative, and the action is faithful). 2025-03-17T05:47:22Z https://yabu.me/nevent1qqsr5ns4tthdqy9np2sr4n4gjdc0hxclg69urpr3t3gc34get5a48uczyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zwu84gnv In reply to <a href='/nevent1qqsr3yql2xtyrg94hrrv5qvh2lv8v7p9vh8qjvd98stm5wyl64nc8uckzgd39'>nevent1q…gd39</a><br/>_________________________<br/><br/>Can you say why you prefer pcloud over Dropbox? I just looked a little and it looks interesting.<br/><br/>For replacing github, have you looked into gitea? 2025-02-02T20:41:15Z https://yabu.me/nevent1qqsy68c9jh070ghlmh5radm5wwggpgyf3slfsq38mdz46kw5syv3e3gzyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zwk7ar7u Just found an English translation of Emmy Noether&#39;s 1921 &#34;Idealtheorie in Ringbereichen&#34; (&#34;Ideal Theory in Rings&#34;): <a href="https://arxiv.org/abs/1401.2577">https://arxiv.org/abs/1401.2577</a><br/><br/>(while editing the wikipedia page on subdirect products - my first wiki edit to add an Emmy Noether reference! Turns out there&#39;s a direct lineage from Noether to Birkhoff&#39;s introduction of subdirect products in universal algebra. Just one more way in which she really revolutionized algebra.)<br/><br/>#math #AlgebraicGeomtry #Algebra #UniversalAlgebra 2024-12-11T00:41:04Z https://yabu.me/nevent1qqsvv4tzsutt0s9ze6cw594k6nl40y4r23pd62zjldq4zqvjeca6easzyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zwhmhlpd We can, and must, do more to protect students and teachers in higher education from the risks of post-COVID condition aka longCOVID <a href="https://theconversation.com/we-can-and-must-do-more-to-protect-students-in-higher-education-from-the-risks-of-post-covid-condition-244244">https://theconversation.com/we-can-and-must-do-more-to-protect-students-in-higher-education-from-the-risks-of-post-covid-condition-244244</a><br/><br/>H/t @aeporreca.org on bsky<br/><br/>#academia #LongCovid #covid #covid19 2024-12-08T21:34:14Z https://yabu.me/nevent1qqsravupmx70l9x86dg0g6lq48f5rjuln779sldumncy6cshrj8ffjqzyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zw9s35d5 Thinking about how AI-generated writing isn&#39;t only poisoning its own training set, it&#39;s also poisoning *ours*.<br/><br/>I&#39;m no expert, but it sure seems like learning good writing often starts with reading good writing. Imagine a generation of kids growing up where half of what they read is AI-generated.<br/><br/>#genAI #writing #reading 2024-10-11T15:13:45Z https://yabu.me/nevent1qqsfzhxpf0vjmppfmrj7yjh76agmafawek2pprcqcqsxcwxa035chagzyzd97zf94nvmmgff53gah2cs7exvs9x2nynch3387lfhdfl9zq2zwjypg6n Apparently I missed that Zhuk posted a *simplified* proof of the CSP Dichotomy Conjecture back in January: <a href="https://arxiv.org/abs/2404.01080">https://arxiv.org/abs/2404.01080</a><br/><br/>I&#39;d really love to understand all of this!<br/><br/>#ComputationalComplexity #complexity #math #UniversalAlgebra 2024-10-04T19:28:22Z