{"paper":{"title":"Three Ehrhart Quasi-polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jes\\'us A. De Loera, Matthias K\\\"oppe, Mich\\`ele Vergne, Nicole Berline, Velleda Baldoni","submitted_at":"2014-10-31T04:29:47Z","abstract_excerpt":"Let $P(b)\\subset R^d$ be a semi-rational parametric polytope, where $b=(b_j)\\in R^N$ is a real multi-parameter. We study intermediate sums of polynomial functions $h(x)$ on $P(b)$, $$\n  S^L (P(b),h)=\\sum_{y}\\int_{P(b)\\cap (y+L)} h(x) \\mathrm dx, $$ where we integrate over the intersections of $P(b)$ with the subspaces parallel to a fixed rational subspace $L$ through all lattice points, and sum the integrals. The purely discrete sum is of course a particular case ($L=0$), so $S^0(P(b), 1)$ counts the integer points in the parametric polytopes.\n  The chambers are the open conical subsets of $R^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8632","kind":"arxiv","version":4},"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"}