Description :
Discussion of current mathematical research. (Moderated)
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The johnson graph
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Hi everyone... Does anyone know of some good papers about the johnson graph ?? This graph has as vertex set all m-subset of {1, ..., n } and two vertices s1, s2 are adjacent if and only if |s1 \cap s2 | = m - 1. I have searhed over the internet but i can only find litte information about this graph... plus »
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Z(t,t^-1) solutions to a(t)p(t)+b(t)q(t)=1
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Greetings. Suppose that p(t) and q(t) are Laurent polynomials with integer coefficients. I am looking for Laurent polynomials with integer coefficients for which a(t)p(t)+b(t)q(t) = 1. Over rationals, not integers, this could be unambiguously determined by the GCD algorithm. However, in integers, the GCD... plus »
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Fourier series question
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Does there exist a nonzero (i.e. not equal to 0 a.e.) Lebesgue integrable function on [0, 2pi] whose Fourier series is 0, i.e. all its Fourier coefficients are 0 ? I don't think the famous Kolmogorov's example answers this question.
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E^(pi*sqrt(163)) and the solvable sextic 5x^6-640320x^5-10x^3+1 = 0
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Hello all, The sextics, 5x^6-15x^5-10x^3+1 = 0 5x^6-32x^5-10x^3+1 = 0 5x^6-96x^5-10x^3+1 = 0 5x^6-960x^5-10x^3+1 = 0 5x^6-5280x^5-10x^3+1 = 0 5x^6-640320x^5-10x^3+1 = 0 have some very interesting properties. 1. I'm sure some will also recognize the sequence {15, 32, 96, 960, 5280, 640320}. (Hint: Their cubes plus 744 are good approximations to... plus »
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Brouwer's choice sequences as a basis for measure theory and probability theory
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In considering problems regarding the foundations of probability, I have thought that Brouwer's choice sequences could be an interesting basis for measure theory and probability theory. The class of choice sequences can be regarded both as the codomain and (in essence) as the domain of probability functions. A such approach could suggest possible solutions... plus »
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Diophantic approximations
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I have a question about approximations of irrational numbers by rationals. Roughly speaking, if x is an irrational, then there exist an infinitely many distinct fractions p/q such that ...of the continued fraction expansion of x. The converse is also true: If p/q is a fraction such that |x - p/q| < 0.5*q^(-2) than p/q... plus »
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Exterior Jet Bundles
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For field theory, when the field is based on natural objects such as differential forms, a more suitable way to encapsulate its Lagrangian appears to be a kind of bundle I've not seen discussed in the literature anywhere -- the exterior jet bundle. Thus, for a 1-form field the configuration variables would comprise a... plus »
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