{"paper":{"title":"On traces of tensor representations of diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.QA","authors_text":"Alexander Schrijver","submitted_at":"2015-01-20T20:17:26Z","abstract_excerpt":"Let $T$ be a set, of {\\em types}, and let $\\iota,o:T\\to\\oZ_+$. A {\\em $T$-diagram} is a locally ordered directed graph $G$ equipped with a function $\\tau:V(G)\\to T$ such that each vertex $v$ of $G$ has indegree $\\iota(\\tau(v))$ and outdegree $o(\\tau(v))$. (A directed graph is {\\em locally ordered} if at each vertex $v$, linear orders of the edges entering $v$ and of the edges leaving $v$ are specified.)\n  Let $V$ be a finite-dimensional $\\oF$-linear space, where $\\oF$ is an algebraically closed field of characteristic 0. A function $R$ on $T$ assigning to each $t\\in T$ a tensor $R(t)\\in V^{*\\o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04945","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"}