{"paper":{"title":"Initial Ideals of Pfaffian Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Colby Long","submitted_at":"2016-10-20T18:15:30Z","abstract_excerpt":"We resolve a conjecture about a class of binomial initial ideals of $I_{2,n}$, the ideal of the Grassmannian, Gr$(2,\\mathbb{C}^n$), which are associated to phylogenetic trees. For a weight vector $\\omega$ in the tropical Grassmannian, $in_\\omega(I_{2,n}) = J_\\mathcal{T}$ is the ideal associated to the tree $\\mathcal{T}$. The ideal generated by the $2r \\times 2r$ subpfaffians of a generic $n \\times n$ skew-symmetric matrix is precisely $I_{2,n}^{\\{r-1\\}}$, the $(r-1)$-secant of $I_{2,n}$. We prove necessary and sufficient conditions on the topology of $\\mathcal{T}$ in order for $in_\\omega(I_{2,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06524","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"}