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A $v$-good sequencing of a DTS$(v)$ is a permutation of the points of the design, say $[x_1 \\; \\cdots \\; x_v]$, such that, for every triple $(x,y,z)$ in the design, it is not the case that $x = x_i$, $y = x_j$ and $z = x_k$ with $i < j < k$. We prove that there exists a DTS$(v)$ having a $v$-good sequencing for all positive integers $v \\equiv 0,1 \\bmod {3}$. Further, for all positive integers $v \\equiv 0,1 \\bmod {3}$, $v \\geq 7$, we prove that there is a DTS"},"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":"1907.11186","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-25T16:46:48Z","cross_cats_sorted":[],"title_canon_sha256":"f805c77b36e075f4f951d288ca8a4a34ddca25eb7b2eb6cfc6a8144a47e7f481","abstract_canon_sha256":"30b37bb1a645e037bba417b05bd11daa28445c74e0fa769b9d7487d0679eb7ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:33.018579Z","signature_b64":"584HJHpumFZ3qpv2lMF4mX2cHkfFf0VbEQb1HoZ6I48bN8M/1R4EdTJTKBZTuV2gCgHVrr0/677bzhPCYdruBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d48a20ca7e6c6890babb36cf4ba02bffa85f07dd6443c8fc505761d3e77c6073","last_reissued_at":"2026-05-17T23:39:33.017917Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:33.017917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Block-avoiding point sequencings of directed triple systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Donald L. Kreher, Douglas R. Stinson, Shannon Veitch","submitted_at":"2019-07-25T16:46:48Z","abstract_excerpt":"A directed triple system of order $v$ (or, DTS$(v)$) is decomposition of the complete directed graph $\\vec{K_v}$ into transitive triples. A $v$-good sequencing of a DTS$(v)$ is a permutation of the points of the design, say $[x_1 \\; \\cdots \\; x_v]$, such that, for every triple $(x,y,z)$ in the design, it is not the case that $x = x_i$, $y = x_j$ and $z = x_k$ with $i < j < k$. We prove that there exists a DTS$(v)$ having a $v$-good sequencing for all positive integers $v \\equiv 0,1 \\bmod {3}$. 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