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I would rather look at this from the opposite end. The key difference between the discrete and continuous cases is that in the discrete case there is a canonical reference measure, namely the counting …

An outstanding result of this sort is the theorem of Tsirelson, MR1487755 Tsirelson, B. Triple points: from non-Brownian filtrations to harmonic measures. Geom. Funct. Anal. 7 (1997), no. 6, 1096–1142 …

I cannot provide you with a reference, but I can sketch with my own derivation (I have a draft somewhere...). First, let $X$ be a zero-truncated multinomial $(n,k)$ random variable (we throw $n$ ball …

The evaluation of the Jones polynomial at $e^{i\pi/3}$ is related to the number of 3-colourings $tri(K)$ of $K$ (see also here) as well as to the topology of the branched double cover $\Sigma(K)$: $$t …

Here's one scientist (not quite a mathematician) who found gold in wastebaskets: I started looking in the trash cans of science for such phenomena [fractal scaling], because I suspected that what I wa …

A somewhat different quote has been attributed to Einstein: http://izquotes.com/quote/226612 (link broken now) https://quotefancy.com/quote/764082/Albert-Einstein-The-physicist-s-greatest-tool-is- …

For prime $q \geq 5$ write the count as $$ \frac1{1152} q (q-1) (q^3 - 21q^2 + 171 q - c_q) $$ where $$ c_q = 483 + 36 \left(\frac{-1}{q}\right) + 64 \left(\frac{-3}{q}\right) + \delta_q. $$ Then for …

Here is the argument I have written up in my thesis. It was suggested to me by my advisor Jarod Alper. We use the fact that a proper monomorphism is a closed immersion (EGA IV, 18.12.6). Furthermore, …

In Two Subspaces (Trans. AMS 1969), Halmos made some useful observations about pairs of subspaces/projections. When $\|p-q\|<1$, this yields in particular that we can assume, up to unitary equivalence …

to your first question : $\int_X \frac{|t|^2}{\|e\|^2 \|s\|^2} \Omega$ is finite, being bounded above by $\sum_{i,j} |\lambda_{ij}|^2 vol_\Omega X$ i have found one paper on google which prove this th …

The following family of examples can be extracted from Lenart and Ray, Some applications of incidence Hopf algebras to formal group theory and algebraic topology (Postscript). Let $B_2$, $B_3$, $B_4$, …

Here is another possible source of tensor products on $\mathbf{Set}$: transferring tensor products from categories $\mathbf{Set}$ is coreflective in. Unfortunately I have no good example. Suppose $(\m …

Edit: I'm leaving the old post below, but before I want to write the proof as suggested by Bruce from his book, which uses the ideas in a more efficient way. Assume that $\|p-q\|<1$, with $p,q\in A$, …

Plausibly we can construct examples from the power series expansion of formal group laws. We can try to write down such examples by writing down nice functions $q(x)$ and hoping that the formal group …

I am adding this because I am surprised no one has mentioned the wonderful CHEVIE package! This does precisely what the OP wants. For example. gap> W:=CoxeterGroup("A",6); CoxeterGroup("A",6) gap> Dis …