Discrete Math Seminar: Petr Skoda and Sophie Burrill
Topic
Petr Škoda -- Title: Obstructions of connectivity 2 for embedding graphs into the torus
Sophie Burrill -- Title: Generating trees for partitions and permutations with no k-nestings
Speakers
Details
Petr Škoda
Abstract:
We study the obstructions (minor-minimal forbidden graphs) for orientable surfaces that have a 2-vertex cut. The building blocks of the obstructions are described. As a consequence, the complete list of 68 obstructions for the torus that have connectivity 2 is constructed.
Sophie Burrill
Abstract: We describea generating tree approach to the enumeration and exhaustive generation of set partitions and permutations with no $k$-nestings. Unlike previous work in the literature using connections of these objects with Young tableaux and restricted lattice walks, our approach deals directly with partitions and permutations diagrams. We detail a generation algorithm that uses only labelsto describe these set partitions and permutations with no $k$-nestings, and provide explicit functional equations for the generating functions, with $k$ as a parameter, getting valuable series results.
