Speaker:  Brett Stevens
Time:     Tuesday Sep 11  14:30
Place:    HP4369 School of Math and Stats, Carleton University
Title:    Queue Compatible Gray Code Orderings.

Abstract:  In "Universal cycles for combinatorial structures," (1992) 
Chung, Diaconis, Graham generalize the notion of deBruijn sequences for
other combinatorial objects besides binary words.  In the article they
propose methods to solve this class of problems and discuss the
difficulty of finding these new objects.  Universal cycles are orderings
of combinatorial objects that are able to be stored in a queue data
structure.  I will discuss two instances of this problem: binary words
and $k$-sets of an $n$-set.  In the first instance we use the Hamming
distance to define proximity (Standard Gray Code metric) instead of the
Shift Opperator (DeBruijn sequence metric).  I will discuss preliminary
results on this topic.  In the second instance I will survey previous
results for $2$-sets, $3$-sets, $4$-sets and $6$-sets.  I will show that
these ordings cannot exist for $k=n-2$.