Shahrooz Janbaz
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 Nov 20 comment Frucht's type theorem for Riemann surface I can not find the paper which is written by Greenberg. Where can I find the paper? Nov 20 comment Frucht's type theorem for Riemann surface @PeterMueller: Actually, as you can see in my question, I am interested in the cases where the dihedral group appears as a kind of group related to the Riemann surface (Manifold). Since I know a little about the Spectrum of compact surface, I asked my question for Riemann surface. But, if there are something for groups corresponding to Riemann manifolds which dihedral groups appears there, I will be so thankful if you give me some references. Nov 20 accepted Frucht's type theorem for Riemann surface Nov 20 comment Frucht's type theorem for Riemann surface Thanks @Goette for you helpful comment. Nov 20 comment Frucht's type theorem for Riemann surface Dear Prof. Rivin, thanks for your helpful answer. Actually, I need such groups which we can correspond to Riemann surface and group of isometries is very interesting. Would you please introduce to me some more references for studying in this direction? Although, I accepted your answer. Nov 20 asked Frucht's type theorem for Riemann surface Oct 19 awarded Popular Question Oct 12 comment Which Dihedral Groups are $\text{CI}$-Groups? @Prof. Royle, thanks for your helpful comment. Actually, I did a deep search about this topic, but always there are some points which professionals know them, but amateurs do not know them. Oct 10 revised Which Dihedral Groups are $\text{CI}$-Groups? I edited tags and corrected a word. Oct 10 asked Which Dihedral Groups are $\text{CI}$-Groups? Oct 1 comment Graph homomorphisms and line graph Let $G=K_3$, the complete graph with three vertices and $H=K_2$. Then $G$ and $H$ is in homomorphism relation. But, $L(G)=G$ and $L(H)=K_1$. If these two latter graphs be in homomorphism relation, then we must have a loop in $L(H)$, which is impossible. I think, if there is at least one edge in $L(G)$ and $L(H)$, your answer is true, Sep 28 comment Number of height-limited rational points on a circle I think if we look at the lattice points on circle $C(hr)$, we can obtain some good upper bound and approximately rate change. So, I think we have $$\pi(hr)^2-\pi\sqrt{2}hr+\frac{\pi}{2}\leq R(hr)\leq \pi(hr)^2+\pi\sqrt{2}hr+\frac{\pi}{2},$$ where $R(hr)$ shows the total number of lattice points in the circle $C(hr)$. I think $R(hr)$ is good lower and upper bound for your question and so when $h$ tend to infinity, the average number of such points you want tend to $\pi$. Sep 27 answered Finite groups with elements of order n Sep 14 answered Advice for PhD Supervisors Sep 2 comment Segal's 1999 Stanford lecture notes on TQFT, where to find them? @GH from MO, so thanks for your guidance. Sep 2 comment Segal's 1999 Stanford lecture notes on TQFT, where to find them? Very nice and helpful command @joro. But, what is the number $2000....$? How can we find it? Aug 31 revised Maximum and minimum diameter of categorical graph product Changed the name to its family. Aug 31 answered Maximum and minimum diameter of categorical graph product Aug 28 comment Existence of finite set of points in the revolving circles @Bogdanov, thanks for your contribution and nice picture. But I still can not understand how your proof work in general! You claim that such distribution of finite points that can be the answer of my main question, there does not exist? yes? Sice, if the final statement of my question be true, this means that such points does not exist. Also, note that in my main question, the two big interior circles have odd parity, not even parity. Aug 27 comment Existence of finite set of points in the revolving circles @Bogdanov, I mentioned about the raduces at the begining of the question. I am so curious to see your picture.