**Title**: Lattice paths between two boundaries

**Abstract: **Dyck paths are lattice paths with steps N=(0,1) and E=(0,1) starting

at (0,0), ending at (n,n), and never going below the diagonal y=x.

Among the many interesting facts known about Dyck paths, one is that

the parameters ‘number of E steps at the end’ and ‘number of returns

to the diagonal’ have a symmetric joint distribution, meaning that to

each Dyck path we can bijectively associate another one where these

parameters are interchanged.

I will show that this symmetry property applies not only to Dyck

paths, but more generally to lattice paths with N and E steps that lie

between any two fixed boundaries. Finally, I will discuss how these

lattice paths are related to other objects in combinatorics, such as

matroids, semistandard Young tableaux and k-triangulations.

This is joint work with Martin Rubey.