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We prove that the necessary conditions are sufficient for existence of two Skolem sequences of order n with 0,1,2,...,n-3 and n pairs in same positions. Further, we apply this result to the fine structure of cyclic two, three and four-fold triple systems, and also to the fine structure of lambda-fold directed triple systems and lambda-fold Mendelsohn triple"},"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":"1303.3421","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-14T12:06:13Z","cross_cats_sorted":[],"title_canon_sha256":"4f839ee40651d343c2b235f0b62b95fdb0bc2294d31be412c98e9dbb861e9267","abstract_canon_sha256":"4ffaec53c7b91ee465ee34757ef03b0f0724c8fea1d3387ace17c906cfd475f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:53.118392Z","signature_b64":"4r7eRc6Fzuvpua455uf8kpTopfRLHpJS8cnSBlBlv9EiAA/TdVDLixrLbLM3PsaQ6WE1+dSxt7yxfx0iL/EUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"864ea13ab0c8f03e438466a25944e0edd582796fa341e2efab9034eee884296b","last_reissued_at":"2026-05-18T03:30:53.115829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:53.115829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The intersection spectrum of Skolem sequences and its applications to lambda fold cyclic triple systems, together with the Supplement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniela Silvesan, Nabil Shalaby","submitted_at":"2013-03-14T12:06:13Z","abstract_excerpt":"A Skolem sequence of order n is a sequence S_n=(s_{1},s_{2},...,s_{2n}) of 2n integers containing each of the integers 1,2,...,n exactly twice, such that two occurrences of the integer j in {1,2,...,n} are separated by exactly j-1 integers. 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