On Lih's conjecture concerning spernerity
Description
Citation
| Title | On Lih's conjecture concerning spernerity |
| Author(s) | D. Horrocks |
| Journal | European Journal of Combinatorics |
| Date | 1999 |
| Volume | 20 |
| Issue | 2 |
| Start page | 131 |
| End page | 148 |
| Abstract | 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. |
| ISSN | 0195-6698 |
Using APA 6th Edition citation style.
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