{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:05Z","timestamp":1753893785697,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper, we construct a bijection from a set of bounded free Motzkin paths to a set of bounded Motzkin prefixes that induces a bijection from a set of bounded free Dyck paths to a set of bounded Dyck prefixes. We also give bijections between a set of bounded cornerless Motzkin paths and a set of $t$-core partitions, and a set of bounded cornerless symmetric Motzkin paths and a set of self-conjugate $t$-core partitions. As an application, we get explicit formulas for the number of ordinary and self-conjugate $t$ core partitions with a fixed number of corners.<\/jats:p>","DOI":"10.37236\/11375","type":"journal-article","created":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T13:09:07Z","timestamp":1679663347000},"source":"Crossref","is-referenced-by-count":0,"title":["Combinatorics on Bounded Free Motzkin Paths and its Applications"],"prefix":"10.37236","volume":"30","author":[{"given":"Hyunsoo","family":"Cho","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JiSun","family":"Huh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hayan","family":"Nam","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaebum","family":"Sohn","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2023,3,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i1p52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i1p52\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T13:09:07Z","timestamp":1679663347000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i1p52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1,13]]}},"URL":"https:\/\/doi.org\/10.37236\/11375","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,3,24]]},"article-number":"P1.52"}}