oh, uh, maybe not. Just explains why derivations appeared when computing automorphism of GA(1,Z/8).
But the three types of edges I do have some sort of an explanation for.
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.
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 Greg Egan (npub12cu…d38p)'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.
The edges between blue and red vertices are then just the 2-fold "covering map" (it's not quite a cover, because it's 2-to-1 but over each odd edge that would be present in the base there's only one blue edge instead of 2).
Joshua Grochow /
npub1nf…ng3kl
2025-03-18 19:29:14
in reply to nevent1q…3nnk
Author Public Key
npub1nf0sjfdvmx76z2dy28d6ky8kfnypfj5ey79uvflh6dm20egszsns0ng3klPublished at
2025-03-18 19:29:14Event JSON
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"content": "oh, uh, maybe not. Just explains why derivations appeared when computing automorphism of GA(1,Z/8).\n\nBut the three types of edges I do have some sort of an explanation for.\n\nThink 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. \n\nBetween 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 nostr:npub12cuzzqzv8e8y7na77a9zv47mx2v6pec60qs5h7takzmv5p0mw0fsmgd38p'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.\n\nThe edges between blue and red vertices are then just the 2-fold \"covering map\" (it's not quite a cover, because it's 2-to-1 but over each odd edge that would be present in the base there's only one blue edge instead of 2).",
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