[Facets-of-complexity] Invitation to Monday Lecture & Colloquium - April 29th 2019

[Ita Brunke <i.brunke@inf.fu-berlin.de>]

You are cordially invited to our next Monday Lecture & Colloquium on April 29th at 14:15 h & 16:00 h at TU Berlin.

Location:

Room MA 041 - Ground Floor
Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin 

Time: Monday, April 29th - 14:15 h

Lecture: Kolja Knauer (Aix-Marseille Université)

Title: Tope graphs of (Complexes of) Oriented Matroids

Abstract:

Tope graphs of Complexes of Oriented Matroids fall into the important class of metric graphs called partial cubes. They capture a variety of interesting graphs such as flip graphs of acyclic orientations of a graph, linear extension graphs of a poset, region graphs of hyperplane arrangements to name a few. After a soft introduction into oriented matroids and tope graphs, we give two purely graph theoretical characterizations of tope graphs of Complexes of Oriented Matroids. The first is in terms of a new notion of excluded minors for partial cube, the second is in terms of classical metric properties of certain so-called antipodal subgraphs. Corollaries include a characterization of topes of oriented matroids due to da Silva, another one of Handa, a characterization of lopsided systems due to Lawrence, and an intrinsic characterization of tope graphs of affine oriented matroids. Moreover, we give a polynomial time recognition algorithms for tope graphs, which solves a relatively long standing open question. I will try to furthermore give some perspectives on classical problems as Las Vergnas simplex conjecture in terms of Metric Graph Theory.

Based on joint work with H.-J; Bandelt, V. Chepoi, and T. Marc.

Coffee & Tea Break :

Room MA 316 - Third Floor [British Reading]

Time: Monday, April 29th - 16:00 h s.t.

Colloquium: Torsten Mütze (Technische Universität Berlin)

Title: Combinatorial generation via permutation languages

Abstract:
In this talk I present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations, which provides a unified view on many known results and allows us to prove many new ones. In particular, we obtain the following four classical Gray codes as special cases: the Steinhaus-Johnson-Trotter algorithm to generate all permutations of an n-element set by adjacent transpositions; the binary reflected Gray code to generate all n-bit strings by flipping a single bit in each step; the Gray code for generating all n-vertex binary trees by rotations due to Lucas, van Baronaigien, and Ruskey; the Gray code for generating all partitions of an n-element ground set by element exchanges due to Kaye. The first main application of our framework are permutation patterns, yielding new Gray codes for different pattern-avoiding permutations, such as vexillary, skew-merged, X-shaped, separable, Baxter and twisted Baxter permutations etc. We also obtain new Gray codes for five different types of geometric rectangulations, also known as floorplans, which are divisions of a square into n rectangles subject to different restrictions. The second main application of our framework are lattice congruences of the weak order on the symmetric group S_n. Recently, Pilaud and Santos realized all those lattice congruences as (n-1)-dimensional polytopes, called quotientopes, which generalize hypercubes, associahedra, permutahedra etc. Our algorithm generates each of those lattice congruences, by producing a Hamilton path on the skeleton of the corresponding quotientope, yielding a constructive proof that each of these highly symmetric graphs is Hamiltonian.

This is joint work with Liz Hartung, Hung P. Hoang, and Aaron Williams.