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To a continued fraction $[a_1,a_2,\\ldots,a_n]$, we associate a snake graph $\\mathcal{G}[a_1,a_2,\\ldots,a_n]$ such that the continued fraction is the quotient of the number of perfect matchings of $\\mathcal{G}[a_1,a_2,\\ldots,a_n]$ and $\\mathcal{G}[a_2,\\ldots,a_n]$. We also show that snake graphs are in bijection with continued fractions.\n  We then apply this co"},"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":"1608.06568","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-23T16:21:42Z","cross_cats_sorted":["math.AC","math.NT"],"title_canon_sha256":"bb641fdc26bf49b37163a467fe71f8df2229c1f82769e0cd13942cc76fa87ff8","abstract_canon_sha256":"dbff5de7bb2f7189b8eae7feb3cdea0023d1b62e4c7a64c24b7e7f63762d88d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:34.131992Z","signature_b64":"BDsF47Tiv2VGaK10/ytE8rXLqE+jZUGXsQ6gA0Tz/+xtlJQ1Ym9DayZ+4rKYMujen4jsDqxSWAxZt2kzoUxRDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53ecf70b3e5db74161d940ea9b3cacc2534814bbd238a9f2257de9a3c52af25c","last_reissued_at":"2026-05-17T23:53:34.131277Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:34.131277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cluster algebras and continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT"],"primary_cat":"math.CO","authors_text":"Ilke Canakci, Ralf Schiffler","submitted_at":"2016-08-23T16:21:42Z","abstract_excerpt":"We establish a combinatorial realization of continued fractions as quotients of cardinalities of sets. 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