43 research outputs found
The limit of a Stanley-Wilf sequence is not always rational, and layered patterns beat monotone patterns
We show the first known example for a pattern for which is not an integer. We find the exact value of the
limit and show that it is irrational. Then we generalize our results to an
infinite sequence of patterns. Finally, we provide further generalizations that
start explaining why certain patterns are easier to avoid than others. Finally,
we show that if is a layered pattern of length , then
holds.Comment: 10 pages, 1 figur
Generalized Descents and Normality
We use Janson's dependency criterion to prove that the distribution of
-descents of permutations of length converge to a normal distribution as
goes to infinity. We show that this remains true even if is allowed to
grow with , up to a certain degree.Comment: 7 page