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We also obtain the number of Hamiltonian paths with one end at a certain outmost vertex of SG(n), with asymptotic behavior $\\frac {\\sqrt{3}(2\\sqrt{3})^{3^{n-1}}}{3} \\times (\\frac {7 \\times 17}{2^4 \\times 3^3})4^n$. The distribution of Hamiltonian paths on SG(n) with one end at a certain outmost vertex and the other end at a"},"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":"0909.5541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-09-30T08:43:18Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3094301ada86ab1dac65de9462c451f168a3a4f9bf419c82213135ac994ea2ad","abstract_canon_sha256":"5fff6885f2e1d0439240a3d86ea36e30df7d02abbbaa60409932c3f3305e1868"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:20.487919Z","signature_b64":"tLdQjrMq61A5x6+Esql7OJE1XsG2AJRD6Q+k5rO/HFn/FhsMAghF3oLNBpFfR9lz5CS22IJwzbRll7gHYMUlDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0dda88b7a3e79aa3ecb8b24516634b6fb7679e870473c611a73f1d39f58a3dd","last_reissued_at":"2026-05-18T04:28:20.487450Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:20.487450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hamiltonian paths on the Sierpinski gasket","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cond-mat.stat-mech","authors_text":"Lung-Chi Chen, Shu-Chiuan Chang","submitted_at":"2009-09-30T08:43:18Z","abstract_excerpt":"We derive exactly the number of Hamiltonian paths H(n) on the two dimensional Sierpinski gasket SG(n) at stage $n$, whose asymptotic behavior is given by $\\frac{\\sqrt{3}(2\\sqrt{3})^{3^{n-1}}}{3} \\times (\\frac{5^2 \\times 7^2 \\times 17^2}{2^{12} \\times 3^5 \\times 13})(16)^n$. We also obtain the number of Hamiltonian paths with one end at a certain outmost vertex of SG(n), with asymptotic behavior $\\frac {\\sqrt{3}(2\\sqrt{3})^{3^{n-1}}}{3} \\times (\\frac {7 \\times 17}{2^4 \\times 3^3})4^n$. 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