A study on prefixes of \(c_2\) invariants (Q776428)

Summary: This paper begins by reviewing recent progress that has been made by taking a combinatorial perspective on the \(c_2\) invariant, an arithmetic graph invariant with connections to Feynman integrals. Then it proceeds to report on some recent calculations of \(c_2\) invariants for two families of circulant graphs at small primes. These calculations support the idea that all possible finite sequences appear as initial segments of \(c_2\) invariants, in contrast to their apparent sparsity on small graphs. For the entire collection see [Zbl 1437.05004].