**Problem of the Week**

**Math Club**

**BUGCAT 2019**

**DST and GT Day**

**Number Theory Conf.**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

seminars:comb:abstract.200410flo

A *matroid* is an axiomatization of the idea of linear dependence. The axioms are also satisfied by algebraic dependence. An abstract matroid is called *algebraic* (over a field F) if it is contained in the matroid of algebraic dependence of an extension field of F (this is called a *full algebraic matroid*). Algebraic matroids have been very hard to study. It is known that there exists a matroid M(p) that is algebraic over fields of characteristic p but not other fields. Lindstöm generalized this type of matroid to M(n) for n ≥ 2, but he found that M(n) is not algebraic if n is even. He conjectured that M(n) is not algebraic if n is any composite number.

I introduce a new kind of matroid called a *harmonic matroid*, of which full algebraic matroids are an example. I prove the conjecture in this more general case.

seminars/comb/abstract.200410flo.txt · Last modified: 2020/01/29 14:03 (external edit)

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial-Share Alike 3.0 Unported