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For signed graphs (which have bidirected orientations), the situation is more subtle. For a finite group $\\Gamma$, let $\\epsilon_2(\\Gamma)$ be the largest integer $d$ so that $\\Gamma$ has a subgroup isomorphic to $\\mathbb{Z}_2^d$. We prove that for every signed graph $G$ and $d \\ge 0$ there is a polynomial $f_d$ so that $f_d(n)$ is the number "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.07369","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-25T16:26:31Z","cross_cats_sorted":[],"title_canon_sha256":"7acceaa282f6530178f109461de48f6788527403f3e8a3bbe0afc7175d08cbb3","abstract_canon_sha256":"774f7b93e84de67f342fb75f03292fb3c10cbb301a9b5c2c399f3e25bf1afc9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:04.737471Z","signature_b64":"poPtXLKaQ72PcnZQQrg+Ao8RBSw0sKL4KwRFPz6Lw9rt5hw8KlvyB1j1W4+0f3RIclE1k4Hwnn7JGSbxn38wDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62820651cbf21e354254463f13220803781a679dc1ec93283a151f975cff70e1","last_reissued_at":"2026-05-18T00:52:04.736922Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:04.736922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on counting flows in signed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edita Rollov\\'a, Matt DeVos, Robert \\v{S}\\'amal","submitted_at":"2017-01-25T16:26:31Z","abstract_excerpt":"Tutte initiated the study of nowhere-zero flows and proved the following fundamental theorem: For every graph $G$ there is a polynomial $f$ so that for every abelian group $\\Gamma$ of order $n$, the number of nowhere-zero $\\Gamma$-flows in $G$ is $f(n)$. 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