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#MarkovNumbers
Latest posts tagged with #MarkovNumbers on Bluesky
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Posts tagged #MarkovNumbers
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YESSSSS!!!!! I am so not gonna lie; my haunted house literally solved this for me like, months ago, and literally has been trying to guide me with the weirdest shit. #MarkovNumbers #Unicity
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Let a = (a'+i) and let b = (b'+j), for integers i and j. If true for a and b, and also true for a' and b', I suspect we have a major contradiction. #MarkovNumbers #Unicity
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I think I just got another one finally for real. When it rains, it pours. #numbertheprimes #markovnumbers #unicity
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Returning back to a #zeckendorf-ish angle for #MarkovNumbers #Unicity always seems to show the most promise. The distinction of that terminal repeat in the pre-Zeckendorf representation *might* be all I need.
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The weird thing here is, for both the Fibonacci and the Pell #MarkovNumbers, L(') proves to be a natural factor of A+(-)B. If one could generalize how this occurs, one would have a very clean explicit expression for Markov Numbers. #Unicity
#ChebyshevPolynomials of the 2nd kind
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A little (tested) progress today. Got my own explicit expressions for #PellNumbers and #FibonacciNumbers that I can use in this alternative approximation for #MarkovNumbers, but still need to justify the approximation / calculate its range of error. #Unicity
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Closest approximation for #MarkovNumbers yet 😁. Used a combination of my own #snakegraph theory and my own #chebyshevpolynomial theory to get there.
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That's the final set-up. I am 100% sure it will work: the missing piece I needed before was the relative ratios. #MarkovNumbers #Unicity
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Done and done. #MarkovNumbers #Unicity #ModularArithmetic #SnakeGraphs #FibonacciNumbers #Fibonacci #Markov #MarkovNumber #ohmygod
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Oh my goodness this is an exciting approach. Verify that this math works out if and only if k=k'. I went back to computing #MarkovNumbers as "perfect matchings of shake graphs" using my formula, and separated summands w diff factors (modulo F(2k+2), effectively). #Unicity
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Cleaned up, but I'm still not convinced of #Unicity. If replication of #MarkovNumbers happens, though, it happens at like depths into the tree, after like numbers of turns. That's really cool. Maybe I can formalize this much and submit.
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#MarkovNumbers #Unicity I've actually got two half proofs now! On the left hand, you've got that the number of turns must be equal. On the right hand, you've got that the number of reflections from "1," "2," or "5" must be equal. I think I can nail this before Saturday, which is "d-day" — 42!!!
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Okay. Now I think we're really getting somewhere. I decided to expand the "b" terms, to force distinction in ' vs. " vs. "' etc. for all terms. #MarkovNumbers #Unicity
Now I need to prove that if we've made an equal number of "turns," the two Markov Numbers can't be equal unless the turns were t
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#MarkovNumbers #Unicity I think! Only 1.x years after I first thought I had it, lol. Just in time for my 42nd birthday!!!
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Yeah. With enough clever wrangling, I reduced this ("given M_N/D and M_N'/D' are sufficiently close") to 3 > 2.618^(k-k') if they're equal. I'm not saying the proof is "in the bag," but Gawd, it's frigging close. #MarkovNumbers #Unicity
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Alright, I've got my problem set up perfectly, I think. Next I'll do the version of the Zeckendorf problem that was sent to me, then tackle this. #MarkovNumbers #Unicity
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Oh my God that's so cool. It keeps a record like a Turing tape. Just write the #MarkovNumbers "base F[2]" (where 21xxx = 100xxx). Come on, Webbie. It really shouldn't be too hard to show #Unicity of every 2-flanked palindrome of pairs of 1s and pairs of 2s. (Last: 10002001.)
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Oh this is sexy. Oh this is VERY sexy. How are you gonna have a matched [even/odd] number of configurations with 2^j for each j for both Snake Graphs? #MarkovNumbers #Unicity
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4 pictures of 1000 words. #MarkovNumbers #Unicity
"Like literally cluster algebra is like the logic structures within the human brain. You can prove anything with it, but it reads like gobbledegook.
"...
"Contextually appropriate structures and symbols, on the other hand, ..."
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...subsequent coefficients upon removing TWO columns at a time from each platform then only add ONE each time to each of the Fibonacci subscripts. #MarkovNumbers #Unicity
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Final solution gives these coefficients to the higher N, lower D number, then waits to coefficient the lower N, higher D number until the platforms are as narrow as those for the higher N, lower D number. That first coefficient is F(2k)^m * F(2k+2)^l, but subsequent... #MarkovNumbers #Unicity
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Now I have a really dangerous approximation. I'm building a false #Markovsnakegraph on a pitched #ChristoffelLatticePath, one that is the stacking of two true #Markovsnakegraphs, and app the number of #perfectmatchings as the product of the two respective #MarkovNumbers times (1+(L2D/N)/(4+L2D/N)).
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