Done and done. #MarkovNumbers #Unicity #ModularArithmetic #SnakeGraphs #FibonacciNumbers #Fibonacci #Markov #MarkovNumber #ohmygod
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#MarkovNumber
Latest posts tagged with #MarkovNumber on Bluesky
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Posts tagged #MarkovNumber
Yes!! You can always read off the "N" value based on the appearance of the representation of the #MarkovNumber M_N/D base U_n(3/2). From there, the "D" value is uniquely defined per the Numerator Conjecture (and basic obviousness). Now how do I turn this into a formal #mathematics proof?! #Unicity
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Is it this simple? #MarkovNumbers #Unicity #CorridorsofTime #MarkovNumber #NumberTheory I just had to find the utility of the "<c"
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It's starting to look like I can assign a #spin and a #mass to each #MarkovNumber (fermion)... based on which directed pair of neighbors (boson) I choose, and for any undirected pair (tachyon), I have the two others (anyon) around which they mutually circulate...
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Alright, this is pretty beautiful. I have gotten the #ChebyshevPolynomials *out* of the equation. They were of magnificent utility while they lasted. Au revoir, #ChebyshevPolynomial... hopefully this will enlighten #MarkovNumber #Unicity somehow. It's a pretty fantastic equation. #MarkovNumbers
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Ugh, I am stuck stuck stuck. I have a feeling that if I can re-build identity II to apply to negative subscripts (using Identity I again) I'll get some sort of weird infinite series that may be of utility. Tick, brain! #MarkovNumbers #Unicity #ChebyshevPolynomial #MarkovNumber #ChebyshevPolynomials
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(2) Given that there is only one such sequence {z_j}, "c" only appears once on the tree.
Like holy fuck. #MarkovNumbers #MarkovNumber #Chebyshev #ChebyshevPolynomial #ChebyshevPolynomials #Unicity
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Okay, actually, this is a total proof outline. Given "c" and treating "b" as a variable, identity III demands strict {z_j} values for each and every "j," in order for the reduced coefficient on each (1.5b)^i to line up with the #ChebyshevPolynomial. #MarkovNumber #MarkovNumbers #Unicity #Chebyshev
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#MarkovNumbers #Unicity #Chebyshev #ChebyshevPolynomial #MarkovNumber this is getting close to the generating function for Chebyshev...
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#MarkovNumbers #Unicity #Chebyshev #ChebyshevPolynomial #MarkovNumber this is getting close to the generating function for Chebyshev...
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Sweet! Hammered out a new #MarkovNumber formula.
sum (i=0 to i = n)
(( z(n-i)*(x(l)/z(0))^i * U(n-i)(3y(m)/2) ))
=
Un*z0
where z(k) is the kth Markov number on a branch; z(0) (which is y(m+1)) is the base of the branch; y(m) is the "host" of that branch; and x(l) is the "host" of y(m)'s branch
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This might be a good angle on what I was originally trying to do. If b' < b, with #MarkovNumber triplets {b,c,d} and {b',c',d}, the existence of the approx-congruency class {x} to [ln b], modulo [ln (3c/2+sqrt(9c2-4)/2)], with integer {e^x}, should cause a conflict with the existence of sim. for '.
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"Number the next orientations by a method each expansion of a #CayleyDickson Construction, Webster. Then watch what #MarkovNumber Tree branches do in terms of sequentially finer rotations, and #Unicity how they cleverly dodge intercepting one another."
I think I may have it. #Chebyshev
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