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Q&A for professional mathematicians
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Hottest Questions Today - MathOverflow
Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, ...
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Let $A$ be a $C^*$-algebra and $(a_{ij}) \in M_n(A)$ be a positive matrix. Does there exist a constant $C \ge 0$ (not depending on the $a_{ij}$) such that $$\lVert(a_{ij})\rVert \le C \Bigl\lVert\s...
Mathoverflow.net news digest
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19 days
Which AI models or architectures can learn and extend the covering algorithm of ...
(I am not announcing new results or asking to verify a proof or a preprint. This post is not a a request to check the work for correctness or an announcement of results. I hope this question meets all of MathOverflow's research standards, if not, please...
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0 days
Percolation long range short range crossover
In 3D bond percolation, the Sak criterion gives a threshold $s = 2 - \eta_\mathrm{SR}$ for the long-range/short-range crossover. Is there a known closed-form relationship between $s_*$, $d$, and $\eta_\mathrm{SR}$ that holds across dimensions, or is...
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0 days
A criterion of monogenic semigroup
Let $D$ a finite semigroup, $card(D)$ odd and for all $x \in D$, $o(x)$ even.
Is it true $D$ is monogenic ? -
0 days
Structural explanation for bottom-strand Betti $\beta_{8,10}=1, \beta_{9,11}=2, ...
1. Setup
Let $k$ be a field (assume $k = \mathbb{Q}$ for concreteness) and let $R = k[x_0, x_1, \ldots, x_9]$ be the polynomial ring in 10 variables, $\mathbb{Z}_{\ge 0}$-graded by $\deg(x_i) = 1$.
Let $\mathrm{CL} : \{0, 1, \ldots, 9\}^2 \to \{0, 1, \ldots, 9\}$ be the symmetric function defined by the following $10 \times 10$ table (the values $0, \ldots, 9$ label abstract operators; the arithmetic substrate is incidental to the question):...
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