This Saturday, February 6, 2010, Dr. Dick Gibbs will be presenting two interesting talks on ”Partitioning” and “Cycle Structure of Permutations.” Following are his descriptions.
I) Partitioning: lines by points; planes by lines; 3-space by planes; etc. There are some nice patterns to be observed here. There’s also the counting of regions formed by chords determined by n points on a circle — it’s (somehow) related to the 4-dimensional partitioning problem.
II) Cycle structure of permutations: lots of counting (and probability) problems here. For example: how many perms. have a given cycle structure? (pretty well-known); for how many perms. does a given pair, triple, etc. occur in the same cycle? (not so well-known — to me anyway!)..