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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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Lexicographic Ramsey theory [PDF]
Journal of Combinatorial Theory, Series A, 1993 AbstractGiven positive integers d and n, there is an integer N such that for every injective map f from {1, …, N}d into R there is a subset A = A1 × A2 × … × Ad of {1, …, N}d such that (1) each Aj has n elements, (2) the restriction of f to A is monotone in each coordinate, (3) there is an ordering of the coordinates such that f on A is lexicographic ...
P. C. Fishburn, Ronald Graham
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A Ramsey Theory of Financial Distortions [PDF]
Journal of Political Economy, 2020 The interest rate on government debt is significantly lower than the rates of return on other assets. From the perspective of standard models of optimal taxation, this empirical fact is puzzling: typically, the government should finance expenditures either through contingent taxes, or by previously-issued state-contingent debt, or by labor taxes, with ...
Wei Cui, Marco Bassetto
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The Ramsey theory of Henson graphs [PDF]
Journal of Mathematical Logic, 2022 Analogues of Ramsey’s Theorem for infinite structures such as the rationals or the Rado graph have been known for some time. In this context, one looks for optimal bounds, called degrees, for the number of colors in an isomorphic substructure rather than one color, as that is often impossible.
Natasha Dobrinen
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Schreier Sets in Ramsey Theory [PDF]
Transactions of the American Mathematical Society, 2005 We show that Ramsey theory, a domain presently conceived to guarantee the existence of large homogeneous sets for partitions on k k -tuples of words (for every natural number k k ) over a finite alphabet, can be extended to one for partitions on Schreier-type sets of words (of every countable ordinal).
Vassiliki Farmaki, S. Negrepontis
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A Result in Dual Ramsey Theory [PDF]
Journal of Combinatorial Theory, Series A, 2002 AbstractWe present a result which is obtained by combining a result of Carlson with the Finitary Dual Ramsey Theorem of Graham–Rothschild.
Lorenz Halbeısen, Pierre Matet
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