On Universal Cycles of k-sets of an n-set

Document Type

Presentation Abstract

Presentation Date

2-14-2002

Abstract

In 1992 Chung, Diaconis and Graham wrote the readable and thoroughly enjoyable "Universal Cycles for Combinatorial Structures". In it they generalize both the definition and construction of de Bruijn cycles to other families of combinatorial objects: permutations, partitions and subset systems. These generalizations resonate with generalizations of Gray Code, being gray codes that are compatible with queue data structures. Hurlbert and Jackson have continued this work solving, among other families, universal cycles for k-sets of n-sets for k = 2, 3, 6 and partially for other k. In their empirical work it was noted and conjectured that a universal cycle for the n – 2-sets of an n-set never exists, even thought the standard necessary conditions are satisfied for all odd n. This was recently proved by Stevens et al. This talk will review the past work, this recent result and the future look at Gray codes or de Bruijn generalizations compatible with different data structures.

Additional Details

Thursday, 14 February 2002
4:10 p.m. in Math 109
Coffee/treats at 3:30 p.m. Math 104 (Lounge)

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