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Q&A for professional mathematicians
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Hottest Questions Today - MathOverflow
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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 $n - 1$
Mathoverflow.net news digest
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0 days
Is every variety equivalent to the dual of a covariety?
A result of Linton and Paré [1] states that (in ZFC), for comonad $D$ on the category $\mathbf{Set}$, the functor $D\text{-Coalg}^{\text{op}} \xrightarrow{U^\text{op}} \text{Set}^{\text{op}} \xrightarrow{2^{(-)}} \text{Set}$ is monadic. In other words...
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0 days
On the Growth Rate of $G(N)$ in Ternary Goldbach Representations
On the Asymptotic Growth Rate of $G(N)$ in Ternary Goldbach Representations
I am investigating a structural refinement of the ternary Goldbach problem, focusing on how closely clustered the three primes in a representation $N = p + q + r$ can be, and what the optimal growth rate is for their maximum difference.... -
1 month
Ways to generalize the Lebesgue inequality in approximation theory
The following relates to what is known as the Lebesgue inequality, which gives an error bound for approximating functions under certain linear mappings, and ways to generalize that inequality.
Let $X$ be a normed linear space and let $Y$ be a subspace of $X$ with a best approximation in norm from that subset to every function in $X$ (e.g., $Y$ is a finite-dimensional linear subspace of $X$). Let $L:X\to Y$ be a bounded and idempotent linear... -
7 years
Reference request: Representing posets by integer divisibility
Does anyone know of an early published reference for the (very easy) fact that all finite posets can be represented as the poset of divisibility of a finite set of integers?
Page 1 of Birkhoff's Lattice Theory (1940) talks about the poset of divisibility of all positive integers, and I assume this must have been known to Birkhoff, but I can't find this specific fact in his book....
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