Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, March 14, 2019, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Torsten Mütze (TU Berlin)

Combinatorial generation via permutation languages

In this talk I present a new and versatile algorithmic framework for generating many different combinatorial classes of objects, based on encoding them as permutations. One of the main applications is the generation of pattern-avoiding permutations (vexillary, skew-merged, separable, clumped, Baxter permutations, and many more). Our algorithm provides a unified view on many known results, such as the binary reflected Gray code for bitstrings, the Steinhaus-Johnson-Trotter algorithm for permutations, the Lucas-Roelants-van Baronaigien Gray code for binary trees, Kaye’s Gray code for set partitions, and it also yields many new Gray codes, in particular for several classes of rectangulations (also known as floorplans). More generally, our algorithm produces a Hamilton path on any lattice quotient of the weak order on permutations. This is joint work with Liz Hartung, Hung Hoang, and Aaron Williams.

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