✦ LIBER ✦

Interval number of special posets and random posets

✍ Scribed by Tom Madej; Douglas B. West

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 473 KB
Volume: 144
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00287-s

No coin nor oath required. For personal study only.

✦ Synopsis

The interval number i(P) of a poset P is the smallest t such that P is a containment poset of sets that are unions of at most t real intervals. For the special poset Bn(k) consisting of the singletons and k-subsets of an n-element set, ordered by inclusion, i(B~(k))---min{k,nk + 1} if In~2-kl >~ n/2-(n/2) 1/3. For bipartite posets with n elements or n minimal elements, i(P) <~ r n/(lg n -lglg n) ] + 1. Finally, the fraction of the n-element posets having interval number between (1 -e) n/8 lg n and (3/2) ([" n/lg n -lg lg n) ] + 1) approaches 1 as n -~ oo (using the Kleitman-Rothschild model of random posets).

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