{"paper":{"title":"Erd\\H{o}s-Ko-Rado theorems on the weak Bruhat lattice}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Glenn Hurlbert, Karen Meagher, Susanna Fishel, Vikram Kamat","submitted_at":"2019-04-02T14:04:32Z","abstract_excerpt":"Let ${\\mathscr L}=(X,\\preceq)$ be a lattice. For ${\\cal P}\\subseteq X$ we say that ${\\cal P}$ is $t$-{\\it intersecting} if ${\\sf rank}(x\\wedge y)\\ge t$ for all $x,y\\in{\\cal P}$. The seminal theorem of Erd\\H{o}s, Ko and Rado describes the maximum intersecting ${\\cal P}$ in the lattice of subsets of a finite set with the additional condition that ${\\cal P}$ is contained within a level of the lattice. The Erd\\H{o}s-Ko-Rado theorem has been extensively studied and generalized to other objects and lattices.\n  In this paper, we focus on intersecting families of permutations as defined with respect t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01436","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"}