Nested chain partitions of Hamiltonian filters
Description
Citation
| Title | Nested chain partitions of Hamiltonian filters |
| Author(s) | D. Horrocks |
| Journal | Journal of Combinatorial Theory Series A |
| Date | 1998 |
| Volume | 81 |
| Issue | 2 |
| Start page | 176 |
| End page | 189 |
| Abstract | Let P be a poset, consisting of all sets X subset of or equal to [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 posers and provide further support for a conjecture of Lih. (C) 1998 Academic Press, Inc. |
| ISSN | 0097-3165 |
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