{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:51Z","timestamp":1753893831508,"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>\r\n\r\n\r\nLinear extensions of posets are important objects in enumerative and algebraic combinatorics that are difficult to count in general. Families of posets like Young diagrams of straight shapes and d-complete posets have hook length product formulas to count linear extensions, whereas families like Young diagrams of skew shapes have determinant or positive sum formulas like the Naruse hook-length formula from 2014. In 2020, Garver et. al. gave determinant formulas to count linear extensions of a family of posets called mobile posets that refine d-complete posets and border strip skew shapes. We give a Naruse type hook-length formula to count linear extensions of such posets by proving a major index q-analogue. We also a inversion index q-analogue of the Naruse formula for mobile tree posets.\r\n\r\n\r\n<\/jats:p>","DOI":"10.37236\/10444","type":"journal-article","created":{"date-parts":[[2022,9,23]],"date-time":"2022-09-23T14:33:48Z","timestamp":1663943628000},"source":"Crossref","is-referenced-by-count":0,"title":["Naruse Hook Formula for Linear Extensions of Mobile Posets"],"prefix":"10.37236","volume":"29","author":[{"given":"GaYee","family":"Park","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2022,9,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i3p57\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i3p57\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,23]],"date-time":"2022-09-23T14:33:48Z","timestamp":1663943628000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i3p57"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,23]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/10444","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,9,23]]},"article-number":"P3.57"}}