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Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We introduce a class of posets, which includes both ribbon posets (skew shapes) and $d$-complete posets, such that their number of linear extensions is given by a determinant of a matrix whose entries are products of hook lengths. We also give $q$-analogues of this determinantal formula in terms of the major index and inversion statistics. As applications, we give families of tree posets whose numbers of linear extensions are given by generalizations of Euler numbers, we draw relations to Naruse and Okada's positive formulas for the number of linear extensions of skew $d$-complete posets, and we give polynomiality results analogous to those of descent polynomials by Diaz-L\u00f3pez, Harris, Insko, Omar, and Sagan.<\/jats:p>","DOI":"10.1137\/20m1320730","type":"journal-article","created":{"date-parts":[[2021,2,16]],"date-time":"2021-02-16T11:01:10Z","timestamp":1613473270000},"page":"205-233","source":"Crossref","is-referenced-by-count":1,"title":["Counting Linear Extensions of Posets with Determinants of Hook Lengths"],"prefix":"10.1137","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0055-0956","authenticated-orcid":true,"given":"Alexander","family":"Garver","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan","family":"Grosser","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jacob P.","family":"Matherne","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2848-3230","authenticated-orcid":true,"given":"Alejandro","family":"Morales","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,2,16]]},"reference":[{"key":"atypb1","first-page":"300","volume":"61","author":"Aitken A. 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Pak,\n                      Counting Linear Extensions of Restricted Posets\n                      ,https:\/\/arxiv.org\/abs\/1802.06312, 2018."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2018.04.007"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(76)90028-5"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1954-030-1"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.37236\/6251"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(93)90095-P"},{"key":"atypb13","unstructured":"S. Grosser,\n                      Determinant Formulas for Counting Linear Extensions of Tree Posets\n                      , Undergraduate honors thesis, UMass, Amherst, 2018,https:\/\/people.math.umass.edu\/~ahmorales\/mentoring\/thesis_Grosser.pdf."},{"key":"atypb14","unstructured":"P. Jiradilok and T. McConville,\n                      Roots of Descent Polynomials and an Algebraic Inequality on Hook Lengths\n                      ,https:\/\/arxiv.org\/abs\/1910.14631, 2019."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2018.11.003"},{"key":"atypb16","unstructured":"D. E. Knuth,\n                      The Art of Computer Programming Volume 3: Sorting and Searching\n                      , Addison-Wesley, Reading, MA, 1998."},{"key":"atypb17","unstructured":"P. A. MacMahon,\n                      Combinatory Analysis Volumes I, II Bound in One Volume\n                      , Dover Phoenix Editions, Dover, Mineola, NY, 2004."},{"key":"atypb18","first-page":"105","author":"M\u00f6hring R. 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