Aryaman Jal: Matroidal and polyhedral aspects of non-nesting rook placements

Abstract

We introduce the rook matroid – a matroid that arises from non-nesting rook placements on a skew shaped board – and study it in relation to transversal matroids, positroids and lattice path matroids. The corresponding polyhedral object – the non-nesting rook polytope – also has a host of interesting properties that we can study using tools from poset theory, matroid theory and discrete optimization. This is joint work with Per Alexandersson and ongoing work with Irem Portakal and Akiyoshi Tsuchiya.