Notable successes for TileScope (aka PermScope) as of June 2019

17 Jun 2019 - Henning

Tilescope is an algorithm for finding and proving structures of permutation classes. When it succeeds it returns a combinatorial specification for the class. In many cases the specification only uses Cartesian products and disjoint unions, and this allows us to turn the specification into a system of equations with a single variable. Some notable examples include:

In other cases more complicated operators are needed, producing a system with a catalytic variable. The system can still be solved using the kernel method or other approaches:

Finally, there are cases when we get systems with several catalytic variables. In these cases the structures represent polynomial-time algorithms that can be used to generate terms