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MD Dialog on: Optimum Savings and Optimal Growth: the Cass-Malinvaud-Koopmans Nexus [PDF]
Stephen E. Spear, Warren Young
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The adjacent Hindman's theorem and the $\mathbb Z$-Ramsey's theorem [PDF]
Bruno Fernando Aceves-Martínez +3 more
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Ramsey's Theorem in Quantum Communication is Like Carnot Cycle in Thermodynamics
Luís Guilherme Miranda Spengler +1 more
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2019
Ramsey theory studies, generally speaking, the following problem: Suppose that a given structure is colored using finitely many colors (equivalently, partition into finitely many pieces). Which combinatorial configurations can be found that are monochromatic, i.e.
Mauro Di Nasso +2 more
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Ramsey theory studies, generally speaking, the following problem: Suppose that a given structure is colored using finitely many colors (equivalently, partition into finitely many pieces). Which combinatorial configurations can be found that are monochromatic, i.e.
Mauro Di Nasso +2 more
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Random Structures & Algorithms, 1992
AbstractSay a graph H selects a graph G if given any coloring of H, there will be a monochromatic induced copy of G in H or a completely multicolored copy of G in H. Denote by s(G) the minimum order of a graph that selects G and set s(n) = max {s(G): |G| = n}. Upper and lower bounds are given for this function. Also, consider the Folkman function fr(n)
Eaton, Nancy, Rödl, Vojtěch
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AbstractSay a graph H selects a graph G if given any coloring of H, there will be a monochromatic induced copy of G in H or a completely multicolored copy of G in H. Denote by s(G) the minimum order of a graph that selects G and set s(n) = max {s(G): |G| = n}. Upper and lower bounds are given for this function. Also, consider the Folkman function fr(n)
Eaton, Nancy, Rödl, Vojtěch
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Combinatorica, 2020
For a polynomial \(P \in \mathbb{Z}[x_1, \ldots ,x_s]\), the equation \(P(x_1, \ldots ,x_s)=0\) is said to be regular if, in any partition \(\mathbb{N}= A_1 \cup \cdots \cup A_r\), there is a solution to this equation with non-identical \(x_1, \ldots ,x_s \in A_i\) for some \(1 \leq i \leq r\). Let \({p} \in \mathbb{Z}[y]\).
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For a polynomial \(P \in \mathbb{Z}[x_1, \ldots ,x_s]\), the equation \(P(x_1, \ldots ,x_s)=0\) is said to be regular if, in any partition \(\mathbb{N}= A_1 \cup \cdots \cup A_r\), there is a solution to this equation with non-identical \(x_1, \ldots ,x_s \in A_i\) for some \(1 \leq i \leq r\). Let \({p} \in \mathbb{Z}[y]\).
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