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Nested Chain Partitions of Hamiltonian Filters

✍ Scribed by David G.C. Horrocks

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
340 KB
Volume
81
Category
Article
ISSN
0097-3165

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✦ Synopsis

Let P be a poset, consisting of all sets X [n]=[1, 2, ..., n] which contain at least one of a given collection F of 2-subsets of [n], ordered by inclusion. By modifying a construction of Greene and Kleitman, we show that if F is hamiltonian, that is, contains [1, 2], [2, 3], ..., [n&1, n] and [1, n], then P is a nested chain order. We examine the Sperner-type properties of such posets and provide further support for a conjecture of Lih.

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