Move-reduced graphs on a torus vs positroid Catalan numbers

Pavel Galashin
University of California, Los Angeles (UCLA)

I will discuss how the same combinatorial dynamics on the affine symmetric group has applications to two seemingly different problems:
(i) Classifying which bipartite graphs on a torus are reduced under square/spider moves, and which reduced graphs are move-equivalent;
(ii) computing positroid Catalan numbers, which are generalizations of Catalan numbers motivated by the geometry of positroid varieties in the Grassmannian, knot theory.
Based on joint works with T. George and T. Lam.


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