{"paper":{"title":"Families of multiweights and pseudostars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Agnese Baldisserri, Elena Rubei","submitted_at":"2015-12-28T20:03:21Z","abstract_excerpt":"Let ${\\cal T}=(T,w)$ be a weighted finite tree with leaves $1,..., n$.For any $I :=\\{i_1,..., i_k \\} \\subset \\{1,...,n\\}$,let $D_I ({\\cal T})$ be the weight of the minimal subtree of $T$ connecting $i_1,..., i_k$; the $D_{I} ({\\cal T})$ are called $k$-weights of ${\\cal T}$. Given a family of real numbers parametrized by the $k$-subsets of $ \\{1,..., n\\}$, $\\{D_I\\}_{I \\in {\\{1,...,n\\} \\choose k}}$, we say that a weighted tree ${\\cal T}=(T,w)$ with leaves $1,..., n$ realizes the family if $D_I({\\cal T})=D_I$ for any $ I $. In [P-S] Pachter and Speyer proved that, if $3 \\leq k \\leq (n+1)/2$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08494","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"}