{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:13Z","timestamp":1753893793275,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We consider the notion of classical parking functions by introducing randomness and a new parking protocol, as inspired by the work presented in the paper ``Parking Functions: Choose your own adventure,'' (arXiv:2001.04817) by Carlson, Christensen, Harris, Jones, and Rodr\u00edguez. Among our results, we prove that the probability of obtaining a parking function, from a length $n$ preference vector, is independent of the probabilistic parameter $p$. We also explore the properties of a preference vector given that it is a parking function and discuss the effect of the probabilistic parameter $p$. Of special interest is when $p=1\/2$, where we demonstrate a sharp transition in some parking statistics. We also present several interesting combinatorial consequences of the parking protocol. In particular, we provide a combinatorial interpretation for the array described in OEIS A220884 as the expected number of preference sequences with a particular property related to occupied parking spots. Lastly, we connect our results to other weighted phenomena in combinatorics and provide further directions for research.<\/jats:p>","DOI":"10.37236\/11649","type":"journal-article","created":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T08:37:16Z","timestamp":1691743036000},"source":"Crossref","is-referenced-by-count":0,"title":["Probabilistic Parking Functions"],"prefix":"10.37236","volume":"30","author":[{"given":"Irfan","family":"Durmi\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alex","family":"Han","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pamela E.","family":"Harris","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rodrigo","family":"Ribeiro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mei","family":"Yin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2023,8,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i3p18\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i3p18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T08:37:34Z","timestamp":1691743054000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i3p18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,11]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/11649","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,8,11]]},"article-number":"P3.18"}}