{"paper":{"title":"The Lecture Hall Cone as a toric deformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lukas Katth\\\"an","submitted_at":"2018-09-05T08:22:10Z","abstract_excerpt":"The Lecture Hall cone is a simplicial cone whose lattice points naturally correspond to Lecture Hall partitions. The celebrated Lecture Hall Theorem of Bousquet-M\\'elou and Eriksson states that a particular specialization of its multivariate Ehrhart series factors in a very nice and unexpected way. Over the years, several proofs of this result have been found, but it is still not considered to be well-understood from a geometric perspective. In this note we propose two conjectures which aim at clarifying this result. Our main conjecture is that the Ehrhart ring of the Lecture Hall cone is actu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01377","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"}