Genre
- Journal Article
Let F be a nonempty collection of subsets of [n] = {1, 2,..., n}, each having cardinality t. Denote by P-F the poser consisting of all subsets of [n] which contain at least one member of F, ordered by set-theoretic inclusion. In 1980, K. W. Lih conjectured that P-F has the Sperner property for all 1 less than or equal to t less than or equal to n and every choice of F. This conjecture is known to be true for t = 1 bur false, in general, for t greater than or equal to 4. In this paper, we prove Lih's conjecture in the case t = 2 We make extensive use of fundamental theorems concerning the preservation of Sperner-type properties under direct products of posers. (C) 1999 Academic Press.
Univ Prince Edward Isl, Dept Math & Comp Sci, Charlottetown, PE C1A 4P3, Canada.
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Source type: Electronic(1)
Language
- English
Subjects
- Mathematics
- PARTIAL ORDERS
- property