Satisfiability and computing van der Waerden numbers.
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Dransfield, Michael R., Liu, Lengning, Marek, Victor W., Truszczyński, Mirosław (2004)
The Electronic Journal of Combinatorics [electronic only]
Bukh, Boris (2009)
The Electronic Journal of Combinatorics [electronic only]
Liu, Rudy X.J. (2009)
The Electronic Journal of Combinatorics [electronic only]
Bergelson, V., Leibman, A. (1999)
Annals of Mathematics. Second Series
Bevan, David (2006)
The Electronic Journal of Combinatorics [electronic only]
Grolmusz, Vince (2002)
The Electronic Journal of Combinatorics [electronic only]
Anstee, Richard, Ferguson, Ron, Sali, Attila (2001)
The Electronic Journal of Combinatorics [electronic only]
Anstee, R.P., Kamoosi, N. (2007)
The Electronic Journal of Combinatorics [electronic only]
Teresa Bigorajska, Henryk Kotlarski (2002)
Fundamenta Mathematicae
We prove a version of the Ramsey theorem for partitions of (increasing) n-tuples. We derive this result from a version of König's infinity lemma for ξ-large trees. Here ξ < ε₀ and the notion of largeness is in the sense of Hardy hierarchy.
J. Töröcsik, J. Pack (1994)
Discrete & computational geometry
Landman, Bruce, Robertson, Aaron, Culver, Clay (2005)
Integers
Exoo, Geoffrey (1998)
The Electronic Journal of Combinatorics [electronic only]
C. Henson, Nigel Kalton, N. Peck, Ignác Tereščák, Pavol Zlatoš (1997)
Studia Mathematica
We prove that every bounded, uniformly separated sequence in a normed space contains a “uniformly independent” subsequence (see definition); the constants involved do not depend on the sequence or the space. The finite version of this result is true for all quasinormed spaces. We give a counterexample to the infinite version in for each 0 < p < 1. Some consequences for nonstandard topological vector spaces are derived.
Yahya Ould Hamidoune (2000)
Acta Arithmetica
Manning, Gregory M. (1995)
Electronic Research Announcements of the American Mathematical Society [electronic only]
Kamat, Vikram (2011)
The Electronic Journal of Combinatorics [electronic only]
Gábor Hegedűs, Lajos Rónyai (2003)
Open Mathematics
Let n, k, α be integers, n, α>0, p be a prime and q=p α. Consider the complete q-uniform family We study certain inclusion matrices attached to F(k,q) over the field . We show that if l≤q−1 and 2l≤n then This extends a theorem of Frankl [7] obtained for the case α=1. In the proof we use arguments involving Gröbner bases, standard monomials and reduction. As an application, we solve a problem of Babai and Frankl related to the size of some L-intersecting families modulo q.
Flaxman, Abraham, Harrow, Aram W., Sorkin, Gregory B. (2004)
The Electronic Journal of Combinatorics [electronic only]
Bidkhori, Hoda, Huang, ShinnYih (2011)
The Electronic Journal of Combinatorics [electronic only]
Yuejian Peng (2007)
Discussiones Mathematicae Graph Theory
Let r ≥ 2 be an integer. A real number α ∈ [0,1) is a jump for r if for any ε > 0 and any integer m ≥ r, any r-uniform graph with n > n₀(ε,m) vertices and density at least α+ε contains a subgraph with m vertices and density at least α+c, where c = c(α) > 0 does not depend on ε and m. A result of Erdös, Stone and Simonovits implies that every α ∈ [0,1) is a jump for r = 2. Erdös asked whether the same is true for r ≥ 3. Frankl and Rödl gave a negative answer by showing an infinite sequence...
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