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### Matroids, Antimatroids, and the External Order

**Algebra & Discrete Mathematics**

Speaker: | Bryan Gillespie, UC Berkeley |

Related Webpage: | https://math.berkeley.edu/~bgillesp/ |

Location: | 1147 MSB |

Start time: | Mon, Nov 20 2017, 4:15PM |

Las Vergnas's active orders are a collection of posets formed from the bases of a matroid using the classical notion of matroid activity. We will describe a remarkable generalization of the external order which endows the independence complex of a matroid with the structure of an antimatroid, a type of greedoid related to abstract convexity theory. The resulting poset is an EL-shellable refinement of the geometric lattice of flats and exhibits a beautiful interplay between matroid theory and lattice theory. Time permitting, we will characterize such "matroidal join-distributive lattices" among all antimatroids.