Newton polytopes in algebraic combinatorics

Math 669: Combinatorics of Polytopes

These are rather condensed notes, not really proofread or edited, presenting key definitions and results of the course that I taught in Winter 2010 term. Problems marked by ◦ are easy and basic, problems marked by ∗ may be difficult. Typeset by AMS-TEX 1

Algebraic combinatorics

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.

Algebraic Methods in Combinatorics

1. (A result of Bourbaki on finite geometries, from Răzvan) Let X be a finite set, and let F be a family of distinct proper subsets of X. Suppose that for every pair of distinct elements in X, there is a unique member of F which contains both elements. Prove that |F| ≥ |X|. Solution: Let X = [n] and F = {A1, . . . , Am}. We need to show that n ≤ m. Define the m × n incidence matrix A over R by ...

Problems in Algebraic Combinatorics

This is a list of open problems, mainly in graph theory and all with an algebraic flavour. Except for 6.1, 7.1 and 12.2 they are either folklore, or are stolen from other people. AMS Classification Number: 05E99