Il Prof. Einar Steingrimsson (University of Strathclyde, Glasgow, UK) terrà una conferenza dal titolo:
"Some open problems on permutation patterns"
Abstract:
An occurrence of a pattern P in a permutation of integers is a subsequence in the permutation whose letters appear in the same order of size as the letters in P. For example, the pattern 231 occurs in 316245 as 362.
Although patterns appear implicitly in the literature a long way back, the origin of the modern development of the subject is often pinned to Knuth's observation (in the sixties) that permutations sortable through a stack are
precisely those that avoid the pattern 231. In the last couple of decades there has been enormous growth in the field, where lots of enumerative results have been obtained, in particular in enumerating classes of
permutations avoiding certain patterns. The unsolved problems, however, still vastly outnumber the solved ones.
I will explain the basic concepts and results of this theory, and then survey some recent developments. These developments deal, on one hand, with hereditary classes of permutations with respect to pattern avoidance.
On the other they concern properties of topological spaces naturally associated to intervals in the set of all finite permutations, partially ordered by pattern containment. A special case of these topological properties is the Möbius function, which is equivalent to the Euler characteristic of the spaces in question.