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Hsu, Sanming Zhou","submitted_at":"2013-07-29T04:16:13Z","abstract_excerpt":"We prove the existence and give constructions of a $(p(k)-1)$-fold perfect resolvable $(v, k, 1)$-Mendelsohn design for any integers $v > k \\ge 2$ with $v \\equiv 1 \\mod k$ such that there exists a finite Frobenius group whose kernel $K$ has order $v$ and whose complement contains an element $\\phi$ of order $k$, where $p(k)$ is the least prime factor of $k$. Such a design admits $K \\rtimes \\langle \\phi \\rangle$ as a group of automorphisms and is perfect when $k$ is a prime. As an application we prove that for any integer $v = p_{1}^{e_1} \\ldots p_{t}^{e_t} \\ge 3$ in prime factorization, and any"},"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":"1307.7455","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-29T04:16:13Z","cross_cats_sorted":[],"title_canon_sha256":"c279afeab32cd8b859817733606e4cf114958ed18cc3d3fbf5c5307767070d2b","abstract_canon_sha256":"431d3abdd014a3f7f87a9a93df266a31243bd1e898b2dc79c2cff4c760b03bca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:47.831589Z","signature_b64":"oBO9OAchJ6dlhNcnBE8LjS0/zb9A1QExqtN86IvVMZ1w/KyYAF411e9HT6fWJO9sr+MUsah9LMKirEmtgQ/gBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b2d17980f0575b6bb3624b4b3c409c6992ca44cdd1d7d50bf22b7b71c8caa1a","last_reissued_at":"2026-05-18T00:04:47.831055Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:47.831055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resolvable Mendelsohn designs and finite Frobenius groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. 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