Each length k pattern occurs equally often in the set Sn of all permutations of length n, but the same is not true in general for a proper subset of Sn. Miklós Bóna recently proved that if we… (More)

We consider the problem of packing fixed-length patterns into a permutation, and develop a connection between the number of large patterns and the number of bonds in a permutation. Improving upon a… (More)

Over the past few years, a number of studies have suggested that the treatment of major depressive disorder (MDD) with anti-depressants enhancing both noradrenergic as well as serotonergic… (More)

When two patterns occur equally often in a set of permutations, we say that these patterns are equipopular. Using both structural and analytic tools, we classify the equipopular patterns in the set… (More)

We consider the enumeration of pattern-avoiding involutions, focusing in particular on sets defined by avoiding a single pattern of length 4. We directly enumerate the involutions avoiding 1342 and… (More)

The “Fibonacci Dichotomy” of Kaiser and Klazar [15] was one of the first general results on the enumeration of permutation classes. It states that if there are fewer permutations of length n in a… (More)

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PATTERNS IN PERMUTATIONS AND… (More)

A permutation class is said to be deflatable if its simple permutations are contained within a proper subclass. Deflatable classes are often easier to describe, analyze and enumerate than their… (More)