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A Special Case of Completion Invariance for the c2 Invariant of a Graph

Published online by Cambridge University Press:  20 November 2018

Karen Yeats
Karen Yeats*
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON N2L 3G1, e-mail: kayeats@uwaterloo.ca
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Abstract

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The ${{c}_{2}}$ invariant is an arithmetic graph invariant defined by Schnetz. It is useful for understanding Feynman periods. Brown and Schnetz conjectured that the ${{c}_{2}}$ invariant has a particular symmetry known as completion invariance. This paper will prove completion invariance of the ${{c}_{2}}$ invariant in the case where we are over the field with 2 elements and the completed graph has an odd number of vertices. The methods involve enumerating certain edge bipartitions of graphs; two different constructions are needed.

Keywords

05C3105C3081T18c2 invariantFeynman graphedge partitionspanning forestcompletion conjecture
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 6 , 01 December 2018 , pp. 1416 - 1435
Copyright
Copyright © Canadian Mathematical Society 2018

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