# UVictoria Discrete Math Seminar: Amarpreet Rattan

## Topic

Counting lattice paths under a boundary of rational slope by flaws

## Details

Counting lattice paths with unit up and right steps beginning at the origin that are somehow constrained by a boundary is an old problem. When the boundary is the line y=x the celebrated Chung-Feller theorem states the number of paths having k flaws (steps above the boundary) is independent of k. The classic Dyck paths are those with 0 flaws, and the Chung-Feller theorem can be used to give a simple proof of their count.

More recently, we have discovered a similar, though more complicated, result to the Chung-Feller theorem for paths constrained by a line of rational slope. In this talk, I will explain these new results and also explain other recent results on counting lattice paths.

My aim is to have a broadly accessible talk, and I will assume very little prior knowledge in this area.

This is joint work with F. Firoozi and J. Jedwab.

**Scientific, Seminar**

**September 12, 2024**

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