Arithmetic Progressions in Partially Ordered Sets
نویسنده
چکیده
Van der Waerden’s arithmetic sequence theorem in particular, the ‘density version’ of Szemeredi is generalized to partially ordered sets in the following manner. Let w and t be fixed positive integers and E > 0. Then for every sufficiently large partially ordered set P of width at most u’, every subset S of P satisfying ] S] > E 1 PI contains a chain a, , a2, . . . . a, such that the cardinality of the interval [a,, a,, i ] in P is the same for each i. AMS subject classification (1980). 06AlO.
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