{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:58Z","timestamp":1753893838300,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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 $|\\{t\\in \\mathbf{t}\\mid t\\leqslant i\\}|+|\\{c\\in \\mathbf{c}\\mid c\\leqslant i\\}|\\geqslant i$ for all $i$ in $[n]$.\u00a0 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. \u00a0A parking completion corresponds to a set of preferences $\\mathbf{c}$ where all cars park.\r\nWe relate parking completions to enumerating restricted lattice paths and give formulas for both the ordered and unordered variations of the problem by use of a pair of operations termed Join and Split.\u00a0 Our results give a new volume formula for most Pitman-Stanley polytopes, and enumerate the \\emph{signature parking functions} of Ceballos and Gonz\u00e1lez D'Le\u00f3n.<\/jats:p>","DOI":"10.37236\/9194","type":"journal-article","created":{"date-parts":[[2020,6,26]],"date-time":"2020-06-26T00:52:09Z","timestamp":1593132729000},"source":"Crossref","is-referenced-by-count":3,"title":["Enumerating Parking Completions Using Join and Split"],"prefix":"10.37236","volume":"27","author":[{"given":"Ayomikun","family":"Adeniran","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Steve","family":"Butler","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Galen","family":"Dorpalen-Barry","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pamela E.","family":"Harris","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cyrus","family":"Hettle","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingzhong","family":"Liang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeremy L.","family":"Martin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hayan","family":"Nam","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,6,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p44\/8101","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p44\/8101","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,26]],"date-time":"2020-06-26T00:52:25Z","timestamp":1593132745000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i2p44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,12]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,4,3]]}},"URL":"https:\/\/doi.org\/10.37236\/9194","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,6,12]]},"article-number":"P2.44"}}