Translator Disclaimer
2010 Trace diagrams, signed graph colorings, and matrix minors
Steven Morse, Elisha Peterson
Involve 3(1): 33-66 (2010). DOI: 10.2140/involve.2010.3.33

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.

Citation

Download Citation

Steven Morse. Elisha Peterson. "Trace diagrams, signed graph colorings, and matrix minors." Involve 3 (1) 33 - 66, 2010. https://doi.org/10.2140/involve.2010.3.33

Information

Received: 22 June 2009; Revised: 19 December 2009; Accepted: 27 December 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1221.05157
MathSciNet: MR2672501
Digital Object Identifier: 10.2140/involve.2010.3.33

Subjects:
Primary: 05C15, 15A69
Secondary: 16W22, 57M07

Rights: Copyright © 2010 Mathematical Sciences Publishers

JOURNAL ARTICLE
34 PAGES


SHARE
Vol.3 • No. 1 • 2010
MSP
Back to Top