ISSN:
1572-9273
Keywords:
06A10
;
Partially ordered sets
;
Van der Waerden's arithmetic sequence
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Van der Waerden's arithmetic sequence theorem—in particular, the ‘density version’ of Szemerédi—is generalized to partially ordered sets in the following manner. Let w and t be fixed positive integers and ε〉0. Then for every sufficiently large partially ordered set P of width at most w, every subset S of P satisfying |S|≥ε|P| contains a chain a 1, a 2,..., a 1 such that the cardinality of the interval [a i, a i+1] in P is the same for each i.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00346651
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