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Combinatorial partitions of finite posets and lattices —Ramsey lattices (1984)

Nešetřil, Jaroslav ; Rödl, Vojtěch

Springer

Algebra universalis 19 (1984), S. 106-119

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ISSN: 1420-8911

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract It is proved that for every finite latticeL there exists a finite latticeL′ such that for every partition of the points ofL′ into two classes there exists a lattice embeddingf:L→L′ such that the points off(L) are in one of the classes. This property is called point-Ramsey property of the class of all finite lattices. In fact a stronger theorem is proved which implies the following: for everyn there exists a finite latticeL such that the Hasse-diagram (=covering relation) has chromatic number 〉n. We discuss the validity of Ramseytype theorems in the classes of finite posets (where a full discussion is given) and finite distributive lattices. Finally we prove theorems which deal with partitions of lattices into an unbounded number of classes.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01191498

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