Extending results of Christie and Irving, we examine the action of reversals and transpositions on finite strings over an alphabet of size k. We show that determining reversal, transposition or… (More)

We disprove a conjecture of Bultena and Ruskey [1], that all trees which are cyclic graphs of cyclic Gray codes have diameter 2 or 4, by producing codes whose cyclic graphs are trees of arbitrarily… (More)

Unlike most books reviewed in the Intelligencer this is definitely a textbook. It assumes knowledge one might acquire in the first two years of an undergraduate mathematics program – basic… (More)

The Poincaré and Cheeger bounds are two useful bounds for the second largest eigenvalue of a reversible Markov chain. Diaconis and Stroock [1991] and Jerrum and Sinclair [1989] develop versions of… (More)

We describe the behavior of certain families of Markov chains as they approach their stationary distributions. Prior methods do not work well for these chains, which are non-reversible, have… (More)

Abstract. By proving a local limit theorem for higher-order transitions, we determine the time required for necklace chains to be close to stationarity. Because necklace chains, built by arranging… (More)

Extending results of Christie and Irving, we examine the action of reversals and transpositions on finite strings over an alphabet of size k. We show that determining reversal, transposition, or… (More)

Ginsburg and Sands defined a procedure for completely disconnecting graphs: each round, remove at most one edge from each component and at most w edges total. Define fw(g) to be the minimal number of… (More)