Let $f(n)=(1 + (-1)^{1 + n})/2$ (which gives 1, 0, 1, 0 ... as n increases from 1 on) and $\lambda(n)$ be the Liouville lambda function. Can I compute a Dirichlet series for $f(n)\lambda(n)$? I could not find it in the Gould and Shonhiwa catalog of known Dirichlet series, but I am convinced it mu...
Say we have a function $f:\mathbb{Z}_2^n \to \mathbb{R}$, such that $\sum _{x\in \mathbb{Z}_2^n} f(x)^2 = 1$ (so we can think of $\{ f(x)^2\} _{x\in \mathbb{Z}_2^n}$ as a distribution). It is natural to define the entropy of such function $f$ as follows: $$H(f) = -\sum _{x \in \mathbb{Z}_2^n} f(x...
The example I first learned was the following: a 2-D TQFT is equivalent to a Frobenius algebra. This is discussed and stated as a folk theorem by Voronov; later, a careful proof was written up and published by Lowell Abrams. See also the book by Joachim Kock.
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links be replaced to get working links. I do not see this domain listed here: Domains with dead links.
In this post, Justin gives a quote about Raoul Bott that has this line in it: He talked about 'folk' theorems... theorems everyone knew, but were never written down. What are some good/interesting examples of these types of theorems?
In category theory there is a 'folk' model structure on the category Cat, where the weak equivalences are the equivalences of categories. There is a similar model structure on 2Cat, with weak equivalences being equivalences of 2-categories (weak ones, I presume) The former was not written down fo...
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