TiRS graphs and TiRS frames: a new setting for duals of canonical extensions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15410%2F15%3A33157051" target="_blank" >RIV/61989592:15410/15:33157051 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
TiRS graphs and TiRS frames: a new setting for duals of canonical extensions
Original language description
In the paper properties of the graphs that arise as duals of bounded lattices in Ploščica's representation via maximal partial maps into the two-element set are studied. A new concept of TiRS graphs which abstract those duals of bounded lattices is introduced. A one-to-one correspondence is proved between TiRS graphs and so-called TiRS frames, which are a subclass of the class of RS frames introduced by Gehrke in 2006 to represent perfect lattices. This yields a dual representation of finite lattices via finite TiRS frames, or equivalently finite TiRS graphs, which generalizes the famous classical Birkhoff dual representation of finite distributive lattices via finite posets from the 1930s. By using both Ploščica's and Gehrke's representations in tandem, a new construction of the canonical extension of a bounded lattice is presented. Two open problems are formulated which might be of interest to researchers working in this area. The new representation of finite lattice via TiRS graphs
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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