Abstract: In this talk, we will see a close connection between alternation-free sequences of words over the alphabet $\mathbb{Z}_n$ and parametric shortest paths in certain graphs. Turns out, in the case of planar graphs, these are words over the alphabet $\mathbb{Z}_2$.
Also, as an application of alternation-free sequences, we will see that thin grid graphs have small parametric complexity. This shows a dichotomy between thin grids and square grids, as square grids have large parametric complexity.
This is based on joint work with Prof. J. Radhakrishnan.
