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For a prime $p$, let $r(\\mathbb{F}_p^n)$ denote the size of the largest subset of $\\mathbb{F}_p^n$ without a three-term arithmetic progression. Although similar methods have been used to study $\\mathfrak{s}(G)$ and $r(\\mathbb{F}_p^n)$, no direct connection between these quantities has previously been established. We give an upper bound for $\\mathfrak{s}(G"},"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":"1708.09100","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-30T03:53:29Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"bfc7b2a3338de04632ce669576ebabfe80fc8742c46db2d23b01d22c5cd5aaf6","abstract_canon_sha256":"a4d679fa5dade8e8f114e45d75846dc2396c91033f6e551dc37603f422b52876"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:09.515515Z","signature_b64":"tYCDGCz27EwOr3VJrS0uNFN0KS267Aduy1bUuEnVGvkdnlHUIPMA70HgVReFKK/ZdeLIPXW2yrOHjKEekzIfAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b8cc814b29dfc8b103f4025eb1a9ca47996ffa616d33c8ec07f577a07d6801f","last_reissued_at":"2026-05-18T00:18:09.514873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:09.514873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Erd\\H{o}s-Ginzburg-Ziv constants by avoiding three-term arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Jacob Fox, Lisa Sauermann","submitted_at":"2017-08-30T03:53:29Z","abstract_excerpt":"For a finite abelian group $G$, the Erd\\H{o}s-Ginzburg-Ziv constant $\\mathfrak{s}(G)$ is the smallest $s$ such that every sequence of $s$ (not necessarily distinct) elements of $G$ has a zero-sum subsequence of length $\\operatorname{exp}(G)$. For a prime $p$, let $r(\\mathbb{F}_p^n)$ denote the size of the largest subset of $\\mathbb{F}_p^n$ without a three-term arithmetic progression. Although similar methods have been used to study $\\mathfrak{s}(G)$ and $r(\\mathbb{F}_p^n)$, no direct connection between these quantities has previously been established. 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