Graduiertenkolleg: Methods for Discrete Structures

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Monday Lecture and Colloquium

Monday, January 9, 2017

Technische Universität Berlin
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
room MA 041

Lecture - 14:15

Raman Sanyal - Goethe-Universität Frankfurt/M

On the geometric combinatorics of posets

Geometric combinatorics is the art of studying discrete structures by way of geometry. True gems in this area are Stanley's "two poset polytopes". The order polytope and the chain polytope reflect much of the combinatorics of posets in their face structures, their volumes, and their Ehrhart polynomials. In this talk I will discuss four more such polytopes associated to partial orders with applications to permutation statistics, increasing/alternating sequences, and valuations on distributive lattices. On the geometric side, these polytopes make interesting connections (and raises plenty of open questions) to anti-blocking polytopes from combinatorial optimization, compressed and equidissectable polytopes from discrete geometry, and arrangements of tropical min- and max-hyperplanes.

Colloquium - 16:00

Karola Mészáros - Cornell University

Product formulas for volumes of flow polytopes

The flow polytope associated to an acyclic graph is the set of all nonnegative flows on the edges of the graph with a fixed netflow at each vertex. We will examine flow polytopes arising from permutation matrices, alternating sign matrices and Tesler matrices. Our inspiration is the Chan-Robins-Yuen polytope (a face of the polytope of doubly-stochastic matrices), whose volume is equal to the product of the first n Catalan numbers (although there is no known combinatorial proof of this fact!). The volumes of the polytopes we study all have nice product formulas.

Letzte Aktualisierung: 04.01.2017