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Q&A for professional mathematicians
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I hope everyone is doing well. Let $K \subset \mathbb{R}^n$ be a centrally symmetric convex body $(K = -K)$. Denote by $K \mid H$ the orthogonal projection of $K$ onto $H$, where $H$ is an $n - 1$
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Hottest Questions Today - MathOverflow
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Mathoverflow.net news digest
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5 years
Are there any well-known statements independent of NF?And also, are there prerequisites suggesting that NF in any way, to one extent or another, are not covered by the incompleteness theorem?
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11 years
Is the Cayley graph of Thompson's group isolated in the space of vertex-transiti...
Consider Thompson's group (the one commonly referred to as $T$), which is finitely presentable. Consider the Cayley graph, but then forget the coloring and direction on edges. So now we just have an undirected graph. Call this $G$.
Let $B \subset G$ be a ball around some vertex in $G$ of large radius. Since $G$ is vertex-transitive, the choice of vertex is irrelevant. The radius must be large enough that $B$ includes the cycles corresponding to the relations in the presentation... -
15 years
$n$ lines in general position; there are $n-2$ small triangles
Suppose we have $n$ lines in general position in the plane. Prove that there are at least $n-2$ ''small'' triangles. Here a "small" triangle is a triangle that is not contained in any larger triangle.
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8 years
On GCD and LCM of elements in integral domain with Krull-dimension 1
Let $R$ be an integral domain with Krull dimension $1$. If $0\ne a \in R$ is such that for every $b \in R$ , the ideal $Ra \cap Rb$ is principal , then is it true that for every $b\in R$, the ideal $Ra+Rb$ is also principal ?
It is clear that if $0\ne a,b$ and $Ra+Rb=Rd$ , then $Ra \cap Rb=R(ab/d)$. So if we know $Ra \cap Rb =Rc$ and want to prove $Ra+Rb$ is principal, then the unique (upto aasociates) possible candidate for the generator is $ab/c$. I'm unable to say anything...
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