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Colloquium, William T. Trotter, Georgia Institute of Technology
September 11, 2018 @ 11:00 am - 12:00 pm
Title: The Top Ten Theorems in the Combinatorics of Posets
Abstract: The study of finite partially ordered sets as a class of discrete structures worthy of independent interest can be traced back to the now classic 1941 paper of Dushnik and Miller introducing the concept of dimension, and the even more widely recognized 1950 paper of Dilworth which includes his chain partitioning theorem now taught in standard undergraduate discrete mathematics courses. The speaker has now devoted the major fraction of his research career, now spanning nearly 50 years, to research on the combinatorics of posets. At various times in the interim, he has given an invited lecture on the same theme, and this lecture includes connections with the Lov\’asz local lemma, the Ahlswede-Daykin four functions theorem, and the Robertson-Seymour theory of graph minors. The body of knowledge is expanding very quickly with pioneering work being done in the U.S., England, Poland, Germany, Hungary and France.