Completing the c₂ completion conjecture for p=2

2022/06/15 by Simone Hu, Hu, Simone, Karen Yeats +1
Mathematics · Physics and Astronomy · #05C30 (Secondary) #05C31 #05E14 #81T18 (Primary) 81Q30 #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications

paper · pdf · doi:10.48550/arxiv.2206.07223

openalex publication_date 2022/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The c₂-invariant is an arithmetic graph invariant useful for understanding Feynman periods. Brown and Schnetz conjectured that the c₂-invariant has a particular symmetry known as completion invariance. This paper will prove completion invariance of the c₂-invariant in the p=2 case, extending previous work of one of us. The methods are combinatorial and enumerative involving counting certain partitions of the edges of the graph.

Related

• A special case of completion invariance for the c₂ invariant of a graph
• A study on prefixes of c₂ invariants
• Properties of c₂ invariants of Feynman graphs
• A few c₂ invariants of circulant graphs
• A result on the c₂ invariant for powers of primes