Avoiding monochromatic maximal antichains

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dc.contributor.advisorWoodrow, Robert E.
dc.contributor.authorGoddard, Edward Wayne
dc.date.accessioned2005-08-05T16:50:03Z
dc.date.available2005-08-05T16:50:03Z
dc.date.issued1992
dc.descriptionBibliography: p. 72-73.en
dc.description.abstractA vertex coloring of a (possibly infinite) poset P 1s called good iff it leaves no nontrivial maximal antichain in P monochromatic. What is the minimum number of colors for which P admits a good coloring? By extending the result for finite posets, it can be shown that if P is well-founded and contains an element with no maximal antichain above it, then P admits a good three-coloring. For products of chains we exploit properties of cofinal and coinitial sequences to obtain good two-colorings in certain cases, the covering chain and club coloring results. As well, we introduce the concept of half-maximal antichain for its potential applications and its own merit. While attempting to extend the positive results thus far obtained, we found examples that violated the conditions of those results. At this point we are unable to determine the number of colors required by such examples.
dc.format.extentvii, 73 leaves ; 30 cm.en
dc.identifier.citationGoddard, E. W. (1992). Avoiding monochromatic maximal antichains (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/19720en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/19720
dc.identifier.isbn0315791632en
dc.identifier.lccQA 171.485 G63 1992en
dc.identifier.urihttp://hdl.handle.net/1880/31032
dc.language.isoeng
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subject.lccQA 171.485 G63 1992en
dc.subject.lcshPartially ordered sets
dc.titleAvoiding monochromatic maximal antichains
dc.typemaster thesis
thesis.degree.disciplineMathematics and Statistics
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameMaster of Science (MSc)
ucalgary.item.requestcopytrue
ucalgary.thesis.accessionTheses Collection 58.002:Box 820 520535244
ucalgary.thesis.notesoffsiteen
ucalgary.thesis.uarcreleaseyen
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