{"paper":{"title":"Hypergeometric Expressions for Generating Functions of Walks with Small Steps in the Quarter Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.CO","authors_text":"Alin Bostan, Fr\\'ed\\'eric Chyzak, Lucien Pech, Manuel Kauers, Mark van Hoeij","submitted_at":"2016-06-09T14:56:04Z","abstract_excerpt":"We study nearest-neighbors walks on the two-dimensional square lattice, that is, models of walks on $\\mathbb{Z}^2$ defined by a fixed step set that is a subset of the non-zero vectors with coordinates 0, 1 or $-1$. We concern ourselves with the enumeration of such walks starting at the origin and constrained to remain in the quarter plane $\\mathbb{N}^2$, counted by their length and by the position of their ending point. Bousquet-M\\'elou and Mishna [Contemp. Math., pp. 1--39, Amer. Math. Soc., 2010] identified 19 models of walks that possess a D-finite generating function; linear differential e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02982","kind":"arxiv","version":3},"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"}