2009-04 Trace diagrams, signed graph colorings, and matrix minors

**Trace Diagrams, Signed Graph Colorings, and Matrix Minors** (with Steve Morse), *Involve* **3** (2010), 33-66. arXiv:0903.1373

**Abstract:** Trace diagrams are structured graphs with edges labeled by matrices. Each diagram has an interpretation as a particular multilinear function. We provide a rigorous combinatorial definition of these diagrams using a notion of signed graph coloring, and prove that they may be efficiently represented in terms of matrix minors. Using this viewpoint, we provide new proofs of several standard determinant formulas and a new generalization of the Jacobi determinant theorem.

page revision: 12, last edited: 30 Apr 2010 12:30