{"paper":{"title":"On $r$-cross $t$-intersecting families for weak compositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cheng Yeaw Ku, Kok Bin Wong","submitted_at":"2013-11-07T07:59:32Z","abstract_excerpt":"Let $\\mathbb N_0$ be the set of non-negative integers, and let $P(n,l)$ denote the set of all weak compositions of $n$ with $l$ parts, i.e., $P(n,l)=\\{ (x_1,x_2,\\dots, x_l)\\in\\mathbb N_0^l\\ :\\ x_1+x_2+\\cdots+x_l=n\\}$. For any element $\\mathbf u=(u_1,u_2,\\dots, u_l)\\in P(n,l)$, denote its $i$th-coordinate by $\\mathbf u(i)$, i.e., $\\mathbf u(i)=u_i$. Let $l=\\min(l_1,l_2,\\dots, l_r)$. Families $\\mathcal A_j\\subseteq P(n_j,l_j)$ ($j=1,2,\\dots, r$) are said to be $r$-cross $t$-intersecting if $\\vert \\{ i\\in [l] \\ :\\ \\mathbf u_1(i)=\\mathbf u_2(i)=\\cdots=\\mathbf u_r(i)\\} \\vert\\geq t$ for all $\\mathbf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1813","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"}