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Let $b_{v}=\\frac {v(v-1)}{12}$ and $I_{3}[v]=\\{0,1,...,b_{v}\\}\\setminus\\{b_{v}-7,b_{v}-6,b_{v}-5,b_{v}-4,b_{v}-3,b_{v}-2,b_{v}-1\\}$. Let $J_{3}[v]=\\{k|$ there exist three $S(2,4,v)$ designs with $k$ same common blocks$\\}$. We show that $J_{3}[v]\\subseteq I_{3}[v]$ for any positive integer $v\\equiv1, 4\\ (\\rm mod \\ 12)$ and $J_{3}[v]=I_{3}[v]$, for $ v\\geq49$ and $v=13 $. We find $J_{3}[16]$ completely. Also we determine some values of $J_{3}[v]$ for $\\ v=25,28,37$ and 40.","authors_text":"Nasrin Soltankhah, Saeedeh Rashidi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-21T06:36:46Z","title":"The 3-way intersection problem for S(2, 4, v) designs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4764","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a83a4d862524affcc8e4f9ff8a5ee24d8a61ce05379115afb87e4c57402f3488","target":"record","created_at":"2026-05-18T03:35:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"929a1868fc9c28489f031473aa2f8fe5161375a1700f6906cb4439c0ab3c9209","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-21T06:36:46Z","title_canon_sha256":"b9b1bd531bd925ab3935423e4e093155f2a5f3306ccdced1a3de13b2e7acf913"},"schema_version":"1.0","source":{"id":"1301.4764","kind":"arxiv","version":1}},"canonical_sha256":"bc8aa0e16bdace92f8fb5627ec3c2efe3495cc9bef5dace94977abe6b20411a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc8aa0e16bdace92f8fb5627ec3c2efe3495cc9bef5dace94977abe6b20411a0","first_computed_at":"2026-05-18T03:35:55.716852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:55.716852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b7hYax1qpCCOAcc875jGkrslgYqGHrzKNqA2HOkoqZ7W87hueXI5dOsTHQhCifbEfoDI/0rbyI/jgUG9hWRcCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:55.717710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a83a4d862524affcc8e4f9ff8a5ee24d8a61ce05379115afb87e4c57402f3488","sha256:447f8b2983a636264aff3b2a7907b49b756374288a40e4dab3d23341a198346a"],"state_sha256":"17c632640dbecd4a6dab77b08e634ba913e3c9623d9dee1629cb5a7ff7012fbb"}