{"paper":{"title":"A strengthened inequality of Alon-Babai-Suzuki's conjecture on set systems with restricted intersections modulo p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gennian Ge, Hengjia Wei, Xin Wang","submitted_at":"2017-01-03T04:58:58Z","abstract_excerpt":"Let $K=\\{k_1,k_2,\\ldots,k_r\\}$ and $L=\\{l_1,l_2,\\ldots,l_s\\}$ be disjoint subsets of $\\{0,1,\\ldots,p-1\\}$, where $p$ is a prime and $A=\\{A_1,A_2,\\ldots,A_m\\}$ be a family of subsets of $[n]$ such that $|A_i|\\pmod{p}\\in K$ for all $A_i\\in A$ and $|A_i\\cap A_j|\\pmod{p}\\in L$ for $i\\ne j$. In 1991, Alon, Babai and Suzuki conjectured that if $n\\geq s+\\max_{1\\leq i\\leq r} k_i$, then $|A|\\leq {n\\choose s}+{n\\choose s-1}+\\cdots+{n\\choose s-r+1}$. In 2000, Qian and Ray-Chaudhuri proved the conjecture under the condition $n\\geq 2s-r$. In 2015, Hwang and Kim verified the conjecture of Alon, Babai and Su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00585","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}