{"paper":{"title":"Generating functions and triangulations for lecture hall cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjamin Braun, Carla D. Savage, Matthias Beck, Matthias K\\\"oppe, Zafeirakis Zafeirakopoulos","submitted_at":"2015-08-19T12:42:23Z","abstract_excerpt":"We investigate the arithmetic-geometric structure of the lecture hall cone \\[ L_n \\ := \\ \\left\\{\\lambda\\in \\mathbb{R}^n: \\, 0\\leq \\frac{\\lambda_1}{1}\\leq \\frac{\\lambda_2}{2}\\leq \\frac{\\lambda_3}{3}\\leq \\cdots \\leq \\frac{\\lambda_n}{n}\\right\\} . \\] We show that $L_n$ is isomorphic to the cone over the lattice pyramid of a reflexive simplex whose Ehrhart $h^*$-polynomial is given by the $(n-1)$st Eulerian polynomial, and prove that lecture hall cones admit regular, flag, unimodular triangulations. After explicitly describing the Hilbert basis for $L_n$, we conclude with observations and a conject"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04619","kind":"arxiv","version":2},"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"}