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Greene-Kleitman's theorem for infinite posets

โœ Scribed by Ron Aharoni; Vladimir Korman

Publisher
Springer Netherlands
Year
1992
Tongue
English
Weight
514 KB
Volume
9
Category
Article
ISSN
0167-8094

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โœฆ Synopsis

It IS proved that If (Y, <) IS a poset with no Infinite chain and k IS a positive integer, then there exist a partition of .Jp into disjoint chains C, and disjoint antichains A,, A,. , A,., such that each chain C, meets min (k, IC, I) antichams A,. We make a 'dual' conjecture, for which the case k = 1 is: if (a, <) is a poset with no infinite antichain.

then there exist a partition of d into antichains A, and a chain C meetmg all A,. This comecture is proved when the maximal size of an antichain in d is 2.

Mathematics

Subject Classification (1991). 06A06.

๐Ÿ“œ SIMILAR VOLUMES

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## Abstract Greene's Theorem states that the maximum cardinality of an optimal __k__โ€path in a poset is equal to the minimum __k__โ€norm of a __k__โ€optimal coloring. This result was extended to all acyclic digraphs, and is conjectured to hold for general digraphs. We prove the result for general dig