A Special Case of Completion Invariance for the c 2 Invariant of a Graph

Yeats, Karen

Canadian journal of mathematics, Tome 70 (2018) no. 6, pp. 1416-1435

Résumé

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.

Détail

DOI : 10.4153/CJM-2018-006-5

Mots-clés : 05C31, 05C30, 81T18, c 2 invariant, Feynman graph, edge partition, spanning forest, completion conjecture

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