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Quasi-polynomials classically -- and \"reasonably\" -- appear in Ehrhart theory and in other contexts where one examines a family of polyhedra, parametrized by a variable t, and defined by linear inequalities of the form a_1x_1+...+a_dx_d <= b(t).\n  Recent results of Chen, Li, Sam; Calegari, Walker; and Roune, Woods show a quasi-polynomial structure in several problems where the a_i are also allowed to vary with t. We discuss the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1308.4694","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-21T20:10:28Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"2d5a2e912e1a56ad312c8bc76b6a798c8c2344a32172a0c669666dff5c107cfe","abstract_canon_sha256":"a3bc912194324bfbd8a5e3274ee5a9cfba6a761ae5394aa309a536329a6592a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:26.594950Z","signature_b64":"/WcKwqfjZjXb0tcAyE9o7duEy9ZWLUU0P0mdlo0sH0gBJ8Z/lQ+ApTLga7ndJ9xZTJkOBIm9i7hvVgn8T9uoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b147710142593b760e1e58bb46894ebff0a8a18e51a5b3eedc464705d5aef78","last_reissued_at":"2026-05-18T02:57:26.594414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:26.594414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The unreasonable ubiquitousness of quasi-polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Kevin Woods","submitted_at":"2013-08-21T20:10:28Z","abstract_excerpt":"A function g, with domain the natural numbers, is a quasi-polynomial if there exists a period m and polynomials p_0,p_1,...,p_{m-1} such that g(t)=p_i(t) for t=i mod m. Quasi-polynomials classically -- and \"reasonably\" -- appear in Ehrhart theory and in other contexts where one examines a family of polyhedra, parametrized by a variable t, and defined by linear inequalities of the form a_1x_1+...+a_dx_d <= b(t).\n  Recent results of Chen, Li, Sam; Calegari, Walker; and Roune, Woods show a quasi-polynomial structure in several problems where the a_i are also allowed to vary with t. 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