Probability, statistics and combinatorics: Tanglegrams and inducibility

  • Date:
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Stephan Wagner
  • Contact person: Fiona Skerman
  • Seminarium

Abstract:

A tanglegram is a structure that consists of two binary trees of the same size whose leaves are connected by a perfect matching. I will review results on the enumeration of tanglegrams, properties of random tanglegrams, planarity, and the concept of inducibility of trees, which was used to obtain bounds on the crossing number of random tanglegrams. The inducibility measures how many copies of a "small" tree can be contained inside a "large" tree. I will conclude with a number of open problems and potential future projects.