dc.contributor.advisor | Emamy-K., M. Reza | |
dc.contributor.author | Meléndez Ríos, Gustavo | |
dc.date.accessioned | 2022-07-14T21:59:21Z | |
dc.date.available | 2022-07-14T21:59:21Z | |
dc.date.issued | 2022-04-26 | |
dc.identifier.uri | https://hdl.handle.net/11721/2864 | |
dc.description.abstract | This thesis proposes two new classes of lattices: <em>ST</em>-distributive and <em>ST</em>-modular lattices. The idea is to define relative distributive and modular properties that are satisfied by some elements over two subsets <em>S</em> and <em>T</em> of a given lattice <em>L</em>. These new classes include the usual distributive and modular lattices. Our main results are (1) establishing some basic properties, (2) completely characterizing the maximal <em>S</em> and <em>T</em> (with some restrictions) to form <em>ST</em>-distributive lattices in the lattice families <strong>M</strong><sub>n</sub> and <strong>M</strong><sub>n,n</sub>, and (3) presenting an application of <em>ST</em>-modular lattices to convex sets. This application has been the first example of <em>ST</em>-modularity and the original motivation of our work [7]. All this extends our work in [10]. In addition, we discuss two other problems with new results. First, we present two shortcuts to the <strong>M</strong><sub>3</sub>-<strong>N</strong><sub>5</sub> Theorem proof in [5, 4] and design two methods to compare the lengths of the three proofs [11]. Second, we introduce a poset on the cut-complexes of the 4-cube and show that it is a distributive lattice [9]. | en_US |
dc.language.iso | en_US | en_US |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 United States | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/us/ | * |
dc.subject | Cut-complexes | en_US |
dc.subject | Birkhoff's Representation Theorem | en_US |
dc.subject | Hasse diagrams | en_US |
dc.subject | Posets | en_US |
dc.subject.lcsh | Convex polytopes | en_US |
dc.subject.lcsh | Lattice theory | en_US |
dc.subject.lcsh | Lattices, Distributive | en_US |
dc.subject.lcsh | Modular lattices | en_US |
dc.title | ST-distributive and ST-modular lattices | en_US |
dc.type | Thesis | en_US |
dc.rights.holder | © 2022 Gustavo A. Meléndez Ríos | en_US |
dc.contributor.committee | Medina Rivera, Luis A. | |
dc.contributor.committee | Rubio Canabal, Ivelisse | |
dc.contributor.campus | University of Puerto Rico, Río Piedras Campus | en_US |
dc.description.graduationSemester | Spring (2nd Semester) | en_US |
dc.description.graduationYear | 2022 | en_US |
thesis.degree.discipline | Maths | en_US |
thesis.degree.level | M.S. | en_US |