Problems in Algebraic Combinatorics

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

Positivity Problems and Conjectures in Algebraic Combinatorics

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 ...