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Small lattices

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Item Summary

Title:Small lattices
Authors:Heeney, Xiang Xia Huang
Contributors:Freese, Ralph (advisor)
Keywords:Lattice theory.
Date Issued:2000
Publisher:University of Hawaii at Manoa
Abstract: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.
Description:viii, 87 leaves, bound : ill. ; 29 cm.
Thesis (Ph. D.)--University of Hawaii at Manoa, 2000.
Pages/Duration:viii, 87 leaves
URI:http://hdl.handle.net/10125/25936
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.
Appears in Collections: Ph.D. - Mathematics
Ph.D. Dissertations- Mathematics Department


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