{"paper":{"title":"On the (co)homology of the poset of weighted partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michelle L. Wachs, Rafael S. Gonz\\'alez D'Le\\'on","submitted_at":"2013-09-21T19:56:38Z","abstract_excerpt":"We consider the poset of weighted partitions $\\Pi_n^w$, introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The maximal intervals of $\\Pi_n^w$ provide a generalization of the lattice $\\Pi_n$ of partitions, which we show possesses many of the well-known properties of $\\Pi_n$. In particular, we prove these intervals are EL-shellable, we show that the M\\\"obius invariant of each maximal interval is given up to sign by the number of rooted trees on on node set $\\{1,2,\\dots,n\\}$ having a fixed number of descents, we find combinatorial bases for homology and cohomo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5527","kind":"arxiv","version":3},"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"}