Eric Nitardy
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 Apr22 comment Enigma : of Wizards, Dwarves and Hats I believe the problem statement precludes any communication once the dwarves decide on a strategy or, at least, that is the intention behind the questioners P.S. section. Apr22 comment Enigma : of Wizards, Dwarves and Hats You may want to add that the dwarves need to have absolutely perfect eye sight with infinite resolution and an uncountably infinite capacity to process what they see. Mar24 comment Chebyshev center = center of mass? @lhf: It seems as though there will be lots of diverse and sundry polygons that work. Take a circle and three distinct points on that circle. Imagine three sides of a polygon lying on the tangent lines for the three points. Now connect those three side by inserting any number of sides between them. You need not worry about symmetry. Just make sure that the weight of the sections of the polygon between the three points of tangency balance so that the centroid is the center of the circle. I'd be more hopeful of an interesting result if the circumcenter and centroid were coincident. Mar24 comment Dirichlet forms @Glassjawed As Didier noted, the gradient is defined on edges. The $\frac{1}{2}$ prevents one from double counting the edges when one sums over the vertices. Mar23 comment Chebyshev center = center of mass? Would not a prism formed from a rotationally symmetric polygon work as well provided it was just long enough to make the incenter unique? Mar23 comment Dirichlet forms You may want to look at Qiaochu Yuan's answer to this question on the discrete Laplacian. He describes the discrete Lapacian on a regular lattice. You appear to be looking at what amounts to a weighted graph. In that case, you need to know whether $x$ and $y$ are edge connected and how 'strongly'. You need $K(x,y)$ for that. Mar22 comment $2$ equations with $4$ variables It appears that you also need to make sure $b>0$ is accounted for in your solution area. Should it be $\frac{(a-1)^2}{4} \gt b \gt \max(0, a-2)$ and $3 \gt a \gt 1$? Mar22 awarded Disciplined Mar22 awarded Organizer Mar19 revised Isosceles trapezoid Struck an erroneous statement Mar19 revised Isosceles trapezoid edited body Mar19 revised Isosceles trapezoid added 122 characters in body; deleted 3 characters in body Mar19 revised Isosceles trapezoid added 201 characters in body Mar19 answered Isosceles trapezoid Mar18 comment compute the fraction of products I do not follow this implication:$$G(z) \frac{1+z}{\lambda z} = G(z/2) \Longrightarrow G(z) = \lambda \frac{z}{(1+z)(1-\frac{z}{2})}.$$ Can you clarify what happened? Mar18 comment The discrete Fourier transform of a Dirichlet charachter NIST Digital Library of Mathematical Functions has a section on Periodic Number-Theoretic Functions that might be helpful. Mar17 awarded Altruist Mar16 awarded Investor Mar15 comment Estimating the Primarithm Thank you. So roughly, since $n < pog(n^n)$ $$\frac{\log{n}}{\log \log{n}} < pog(n) < 1.5 \frac{\log{n}}{\log \log{n}}$$. Mar15 accepted Estimating the Primarithm