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Anant Godbole, East Tennessee State University

Abstract: A universal cycle generalizes the notion of deBruijn cycles to combinatorial structures such as graphs, subsets, set partitions, venn diagram allocations, etc. In a very real sense, universal cycles are combinatorial designs, though they have not been recognized as such, or studied by the MSC 05BXX community in depth. I will present 10 years’ worth of work, with undergraduates, REU students, and graduate students that has contributed significantly to the body of knowledge on existence of universal cycles for the above-mentioned structures as well as for hypergraphs, naturally labeled posets, words with restrictions, lattice paths, etc.