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Extended Ramsey theory for words representing rationals

Vassiliki Farmaki, Andreas Koutsogiannis (2013)

Fundamenta Mathematicae

Ramsey theory for words over a finite alphabet was unified in the work of Carlson, who also presented a method to extend the theory to words over an infinite alphabet, but subject to a fixed dominating principle. In the present work we establish an extension of Carlson's approach to countable ordinals and Schreier-type families developing an extended Ramsey theory for dominated words over a doubly infinite alphabet (in fact for ω-ℤ*-located words), and we apply this theory, exploiting the Budak-Işik-Pym...

Frankl’s conjecture for large semimodular and planar semimodular lattices

Gábor Czédli, E. Tamás Schmidt (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A lattice L is said to satisfy (the lattice theoretic version of) Frankl’s conjecture if there is a join-irreducible element f L such that at most half of the elements x of L satisfy f x . Frankl’s conjecture, also called as union-closed sets conjecture, is well-known in combinatorics, and it is equivalent to the statement that every finite lattice satisfies Frankl’s conjecture. Let m denote the number of nonzero join-irreducible elements of L . It is well-known that L consists of at most 2 m elements....

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