Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, February 25, 2010, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Anna Gundert

Lattice paths and Lagrangian matroids

We will start with a short introduction to both matroids and Lagrangian matroids, which are a generalization of ordinary matroids. As an example we then consider the Catalan matroid, the set of lattice paths from (0,0) to (2n,0) that stay above the x-axis ("Dyck paths"). Weakening the conditions on this structure, one can consider the set of lattice paths between two fixed paths with a common starting and a common end point, such that one stays above the other. This also yields a matroid.

The class of these matroids ("lattice path matroids", LPMs) can further be generalized by asking for the boundary paths to just have the same length instead of a common end point. This way, one obtains the class of lattice path Lagrangian matroids (LPLMs). Both these classes were studied by A. de Mier and J. Bonin.

If time allows, I will present a result relating LPLMs and LPMs by E.Kim, D. Schymura and A.G.

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