Preface: Geometric and algebraic combinatorics

Algebraic and geometric methods in enumerative combinatorics

Enumerative combinatorics is about counting. The typical question is to find the number of objects with a given set of properties. However, enumerative combinatorics is not just about counting. In “real life”, when we talk about counting, we imagine lining up a set of objects and counting them off: 1, 2, 3, . . .. However, families of combinatorial objects do not come to us in a natural linear ...

Algebraic combinatorics

Enumerative and Algebraic Combinatorics

Enumeration, alias counting, is the oldest mathematical subject, while Algebraic Combinatorics is one of the youngest. Some cynics claim that Algebraic Combinatorics is not really a new subject but just a new name given to Enumerative Combinatorics in order to enhance its (former) poor image, but Algebraic Combinatorics is in fact the synthesis of two opposing trends: abstraction of the concret...

Algebraic Combinatorics in Bayreuth

I should like to give a brief introduction of our group, describe its main activities in the field of Algebraic Combinatorics, and illustrate them by a few typical examples.

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