This conference is devoted to permutation patterns, i.e., the study of permutations with respect to the involvement order. A pattern in a permutation written in one-line notation is a subsequence whose entries have a prescribed relative order. This definition can be re-phrased in various different contexts, e.g. geometrical, where a permutation is identified with its plot, and model-theoretic, where a permutation is taken to be a set with two linear orders defined on it. Of particular interest are the sets of permutations which are closed under involvement. These are precisely the sets of permutations which can be defined by avoiding (i.e. not involving) prescribed sets of permutations ("forbidden patterns"). The conference topics include enumeration questions, algorithmic problems, and applications and generalizations of permutation patterns.
Historically, the study of pattern containment in permutations arose from two independent streams in 1960s and 1970s. One was combinatorial in nature, and concentrated on the enumeration problems for permutations with a small set (size 1 or 2, typically) of short (length up to 4) forbidden patterns. The other was coming from Theoretical Computer Science, and was concerned with sets arising from common sorting mechanisms and their combinations. In the past 10 years or so these two strands have come much closer together, and this interaction has created a new, fast developing area of combinatorics, with significant interactions with Theoretical Computer Science, the Theory of Computability and Complexity, Algebra, and Computational Biology, to name only a few. Apart from the continued interest in sorting mechanisms and enumeration problems, major new strands of research have emerged including the structural theory of classes, the asymptotic behavior of classes, generalized pattern avoidance, packing densities, algorithmic and decidability problems, and geometrical methods.
The eighth international conference on Permutation Patterns (PP2010) was held at Dartmouth College in Hanover, NH, from August 8 to August 13, 2010. The continuing success of the annual PP conferences stems in part from their focus on a vibrant, emerging area of research that contains difficult open problems, yet remains accessible to young mathematicians. The focus of this conference series is unique among international conferences in mathematics. Even though permutation patterns have been present implicitly in the literature for over a century, interest in this subject has exploded in the past two decades, and continues to grow. This is largely due to the interconnections to other areas of mathematics, such as algebra and geometry, and other disciplines, such as computer science, physics, and biology. The two plenary speakers at PP2010 were Nik Ruskuc, from the University of St. Andrews, Scotland, and Richard Stanley, from M.I.T. In addition to these two hour-long presentations, there were 32 contributed half-hour talks, and an open problem session. There were 61 participants, of which 11 were undergraduate students, 19 were graduate students, 18 were junior researchers (postdocs and pre-tenure faculty), and 13 were senior researchers (tenured faculty). This was a record number of participants in the Permutation Patterns conference series. We were especially pleased with the large attendance by students and junior researchers, which provided them with an opportunity to make both domestic and international contacts that are likely have significant value in their future careers. The NSF grant awarded for PP2010 allowed us to support the attendance of the plenary speaker Richard Stanley, as well as the domestic graduate students and junior researchers. ?
