{"paper":{"title":"$t$-Unique Reductions for M\\'esz\\'aros's Subdivision Algebra","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.CO","authors_text":"Darij Grinberg","submitted_at":"2017-04-04T00:07:01Z","abstract_excerpt":"Fix a commutative ring $\\mathbf{k}$, two elements $\\beta,\\alpha\\in\\mathbf{k}$ and a positive integer $n$. Let $\\mathcal{X}$ be the polynomial ring over $\\mathbf{k}$ in the $n(n-1)/2$ indeterminates $x_{i,j}$ for all $1\\leq i<j\\leq n$. Consider the ideal $\\mathcal{J}$ of $\\mathcal{X}$ generated by all polynomials of the form $x_{i,j}x_{j,k}-x_{i,k}(x_{i,j}+x_{j,k}+\\beta)-\\alpha$ for $1\\leq i<j<k\\leq n$. The quotient algebra $\\mathcal{X}/\\mathcal{J}$ (at least for a certain choice of $\\mathbf{k}$, $\\beta$ and $\\alpha$) has been introduced by Karola M\\'esz\\'aros as a commutative analogue of Anato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00839","kind":"arxiv","version":7},"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"}