{"paper":{"title":"Enumerating Parking Completions Using Join and Split","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ayomikun Adeniran, Cyrus Hettle, Galen Dorpalen-Barry, Hayan Nam, Jeremy L. Martin, Pamela E. Harris, Qingzhong Liang, Steve Butler","submitted_at":"2019-12-03T21:29:14Z","abstract_excerpt":"Given a strictly increasing sequence $\\mathbf{t}$ with entries from $[n]:=\\{1,\\ldots,n\\}$, a parking completion is a sequence $\\mathbf{c}$ with $|\\mathbf{t}|+|\\mathbf{c}|=n$ and $|\\{t\\in \\mathbf{t}\\mid t\\le i\\}|+|\\{c\\in \\mathbf{c}\\mid c\\le i\\}|\\ge i$ for all $i$ in $[n]$. We can think of $\\mathbf{t}$ as a list of spots already taken in a street with $n$ parking spots and $\\mathbf{c}$ as a list of parking preferences where the $i$-th car attempts to park in the $c_i$-th spot and if not available then proceeds up the street to find the next available spot, if any. A parking completion correspond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.01688","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1912.01688/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}