This dissertation introduces triple gluing lattices and proves that a triple gluing lattice is small if the key subcomponents are small. Then attention is turned to triple gluing irreducible small lattices. The triple gluing irreducible [Special characters omitted.] lattices are introduced. The conditions which insure [Special characters omitted.] small are discovered. This dissertation also give some triple gluing irreducible small lattices by gluing [Special characters omitted.] 's. Finally, K-structured lattices are introduced. We prove that a K-structured lattice L is triple gluing irreducible if and only if [Special characters omitted.] . We prove that no 4-element antichain lies in u 1 /v1 of a K-structured small lattice. We also prove that some special lattices with 3-element antichains can not lie in u1 /v1 of a K-structured small lattice. / viii, 87 leaves, bound : ill. ; 29 cm. / Thesis (Ph. D.)--University of Hawaii at Manoa, 2000.
| Identifer | oai:union.ndltd.org:UHAWAII/oai:scholarspace.manoa.hawaii.edu:10125/25936 |
| Date | January 2000 |
| Creators | Heeney, Xiang Xia Huang |
| Contributors | Freese, Ralph |
| Publisher | University of Hawaii at Manoa |
| Source Sets | University of Hawaii at Manoa Libraries |
| Language | en-US |
| Detected Language | English |
| Type | Thesis, Text |
| Format | viii, 87 leaves |
| Rights | All UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner. |
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