Results 1 to 10 of about 6,487,048 (191)
Ramsey theory and thermodynamics [PDF]
Heliyon, 2023 Re-shaping of thermodynamics with the graph theory and Ramsey theory is suggested. Maps built of thermodynamic states are addressed. Thermodynamic states may be attainable and non-attainable by the thermodynamic process in the system of constant mass. We
Nir Shvalb +3 more
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New directions in Ramsey theory [PDF]
Discrete Mathematics Letters, 2021 New developments in the study of Ramsey theory for graphs are described. In particular, it is discussed how Ramsey theory has evolved from classical Ramsey numbers to more general Ramsey numbers, bipartite Ramsey numbers, k-Ramsey numbers, s-bipartite ...
Gary Chartrand, Ping Zhang
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More on lines in Euclidean Ramsey theory [PDF]
Comptes Rendus. Mathématique, 2023 Let $\ell _m$ be a sequence of $m$ points on a line with consecutive points at distance one. Answering a question raised by Fox and the first author and independently by Arman and Tsaturian, we show that there is a natural number $m$ and a red/blue ...
Conlon, David, Wu, Yu-Han
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Dynamics, 2023 Ramsey theory constitutes the dynamics of mechanical systems, which may be described as abstract complete graphs. We address a mechanical system which is completely interconnected by two kinds of ideal Hookean springs.
Nir Shvalb +3 more
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European Journal of Combinatorics, 2021 Given a metric space $\mathcal{M}$ that contains at least two points, the chromatic number $χ\left(\mathbb{R}^n_{\infty}, \mathcal{M} \right)$ is defined as the minimum number of colours needed to colour all points of an $n$-dimensional space $\mathbb{R}^n_{\infty}$ with the max-norm such that no isometric copy of $\mathcal{M}$ is monochromatic.
Frankl, Nóra +2 more
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Finite Ramsey theory through category theory [PDF]
L’Enseignement Mathématique, 2022 We present a new, category-theoretic point of view on finite Ramsey theory. Our aims are as follows: We also provide some concrete illustrations of the general method.
S. Solecki
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MONOID ACTIONS AND ULTRAFILTER METHODS IN RAMSEY THEORY [PDF]
Forum of Mathematics, Sigma, 2019 First, we prove a theorem on dynamics of actions of monoids by endomorphisms of semigroups. Second, we introduce algebraic structures suitable for formalizing infinitary Ramsey statements and prove a theorem that such statements are implied by the ...
SŁAWOMIR SOLECKI
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Complexity of Infinite-Domain Constraint Satisfaction, 2011 G. Chartrand, Ping Zhang
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Fermat's Last Theorem, Schur's Theorem (in Ramsey Theory), and the infinitude of the primes [PDF]
Discrete Mathematics, 2023 Alpoge and Granville (separately) gave novel proofs that the primes are infinite that use Ramsey Theory. In particular, they use Van der Waerden's Theorem and some number theory. We prove the primes are infinite using an easier theorem from Ramsey Theory,
W. Gasarch
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Testing Closeness of Multivariate Distributions via Ramsey Theory [PDF]
Symposium on the Theory of Computing, 2023 We investigate the statistical task of closeness (or equivalence) testing for multidimensional distributions. Specifically, given sample access to two unknown distributions p, q on d, we want to distinguish between the case that p=q versus ||p−q||Ak > є,
Ilias Diakonikolas +2 more
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