Cap set - Wikipedia
In affine geometry, a cap set is a subset of the affine space (the -dimensional affine space over the three-element field) where no three elements sum to the zero vector. The cap set problem is the problem of finding the size of the largest possible cap set, as a function of . [1]
Google DeepMind used a large language model to solve an …
Dec 14, 2023 · The cap set problem is like trying to figure out how many dots you can put down without three of them ever forming a straight line. It’s super niche, but important.
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Simple Set Game Proof Stuns Mathematicians - Quanta Magazine
May 31, 2016 · The rules of the Set game translate neatly into the geometry of the resulting n-dimensional space: Every line in the space contains exactly three points, and three points form a set precisely when they lie on the same line. A cap set, therefore, is a collection of points that contains no complete lines.
The cap set problem and standard diagrams - ScienceDirect
Nov 1, 2021 · The solution to the cap set problem is known for n at most 6. In this paper, we define and apply standard diagrams. These pictures interpret a well-known technique for solving the cap set problem in a new way, allowing conclusions to …
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Cap Set Problem - (Extremal Combinatorics) - Fiveable
The cap set problem is a question in extremal combinatorics that asks about the largest subset of a finite vector space over a finite field, specifically $\mathbb{F}_3^n$, that does not contain any three elements which sum to zero.
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Past and future of the cap set problem - arXiv.org
Aug 6, 2024 · To apply this sort of result, one needs to encode the combinatorial problem under consideration in terms of vanishing of some low-degree polynomial, and then show that the properties of the polynomial (reflecting the original combinatorial problem) are inconsistent with the low-degree condition.
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The Cap Set Problem - SpringerLink
Jul 29, 2020 · In this chapter, we discuss the cap set problem and its relation to transversals in 3-uniform hypergraphs. The card game SET is played with a deck of \(3^n\) cards. On each card is printed n symbols or features. For example, if \(n=4\), then these four features are color, number, shape, and shading.
AMS :: Bulletin of the American Mathematical Society
This expository article covers the history and motivation for the cap set problem and some of the many applications of the technique: from removing triangles from graphs, to rigidity of matrices, and to algorithms for matrix multiplication.
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Cap set - Wikiwand
In affine geometry, a cap set is a subset of (an -dimensional affine space over a three-element field) where no three elements sum to the zero vector. The cap set problem is the problem of finding the size of the largest possible cap set, as a function of . [1]
AI Solves Cap Set Problem For The First Time, DeepMind Claims
Dec 16, 2023 · The cap set problem is a puzzle that involves finding the largest possible set of points in a multidimensional space, such that no three of them are collinear. In other words, no matter how many points you add, you can never form a straight line with any three of them.
Mathematical discoveries from program search with large ... - Nature
Dec 14, 2023 · Applying FunSearch to a central problem in extremal combinatorics—the cap set problem—we discover new constructions of large cap sets going beyond the best-known ones, both in finite ...
[2206.09719] The cap set problem: 41-cap 5-flats - arXiv.org
Jun 20, 2022 · Abstract: An s-cap n-flat, or an n-dimensional cap of size s, is a pair (S,F) where F is an n-dimensional affine space over Z/3Z and the size-s subset S of F contains no triple of collinear points. The cap set problem in dimension n asks for …
Oct 1, 2018 · This expository article covers the history and motivation for the cap set problem and some of the many applications of the technique: from removing triangles from graphs, to rigidity of matrices, and to algorithms for matrix multiplication.
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WMO launches E-learning platform for hazard alerts
The CAP platform is accessible at cap.wmo.int. WMO has developed a set of E-learning resources and courses for the Common Alerting Protocol, which is an internationally-recognized standard for dissemination of warnings of extreme weather hazards to the public and to disaster management authorities. The Common Alerting Protocol (CAP) is adata ...
Saints WR Chris Olave considering wearing Guardian Cap
2 days ago · A Guardian Cap is a type of padding worn over the helmet with the intention of reducing the risk of concussions and head injuries during play. ... Saints' Carr set for return, says he's 'no savior ...
Ready Your Fee Agreements—Fee Cap Increase Takes Effect …
4 days ago · In case you haven’t heard, the fee agreement cap is set to increase to $9,200 on November 30, 2024.In preparation for this change (and in anticipation of the annual increases that will begin starting with the 2026 COLA announcement), we recommend reviewing your current Fee Agreements to ensure that they contain proper escalator language.
Council wants bus fares kept as 'low as possible' after cap hike - BBC
The cap on single bus journeys is set to rise to £3 Cornwall Council says it wants to keep prices for single bus tickets as low as possible after the government announced it planned to raise a ...
Stocks Rise With Payrolls Set to Cap Volatile Week: Markets Wrap
2 days ago · The S&P 500 lost 1.9% and the Nasdaq 100 dropped 2.4% Thursday, their worst sessions since early September. Declines for US equities reflected investor unease over tech giants, including Microsoft ...