{"paper":{"title":"A computational algebraic geometry approach to classify partial Latin rectangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ra\\'ul M. Falc\\'on","submitted_at":"2017-03-31T10:52:55Z","abstract_excerpt":"This paper provides an in-depth analysis of how computational algebraic geometry can be used to deal with the problem of counting and classifying $r\\times s$ partial Latin rectangles based on $n$ symbols of a given size, shape, type or structure. The computation of Hilbert functions and triangular systems of radical ideals enables us to solve this problem for all $r,s,n\\leq 6$. As a by-product, explicit formulas are determined for the number of partial Latin rectangles of size up to six. We focus then on the study of non-compressible regular partial Latin squares and their equivalent incidence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10846","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"}