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We investigate $\\kappa_{r,G}$, the maximum number of sum-free $r$-colorings admitted by subsets of $G$, and our results show a close relationship between $\\kappa_{r,G}$ and largest sum-free sets of $G$. Given a sufficiently large abelian group $G$ of type $I$, i.e., $|G|$ has a prime divisor $q$ with $q\\equiv 2\\pmod 3$. For $r=2,3$ we show that a subset $A\\subset G$ achieves $\\kappa_{r,G}$ if and only if $A$ i"},"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":"1710.08352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-23T15:53:03Z","cross_cats_sorted":[],"title_canon_sha256":"55323e975b7b10026e4d502b0b6158b8cb23f2c3e01f15dbb8fa3d2fd8df0092","abstract_canon_sha256":"047fd62e455257f1c5f820d6531a4aee59b50afa07b1232bfda87d9bbf8a4b24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:16.634005Z","signature_b64":"y4jO4XFUO3G5M5SUtaRiUwyiOAx5JJkeGqiNx/7UHp6xCIBgguap0+CSbZlU5lSgER0NMsCbcEoQbjf/06nJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7baec1c6f7e9be15645b9b351811e59b63254a29c178a3063a90ff8a25b5f2c6","last_reissued_at":"2026-05-18T00:32:16.633278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:16.633278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximum number of sum-free colorings in finite abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrea Jim\\'enez, Hiep H\\`an","submitted_at":"2017-10-23T15:53:03Z","abstract_excerpt":"An $r$-coloring of a subset $A$ of a finite abelian group $G$ is called sum-free if it does not induce a monochromatic Schur triple, i.e., a triple of elements $a,b,c\\in A$ with $a+b=c$. We investigate $\\kappa_{r,G}$, the maximum number of sum-free $r$-colorings admitted by subsets of $G$, and our results show a close relationship between $\\kappa_{r,G}$ and largest sum-free sets of $G$. Given a sufficiently large abelian group $G$ of type $I$, i.e., $|G|$ has a prime divisor $q$ with $q\\equiv 2\\pmod 3$. 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