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The corresponding dual problem of size distribution under large dimension is also addressed and follows a quadratic type normal limit law. These results represent the first of their kind and solve two open questions raised in the combinatorial literature. They are presented in a general framework where the entries of the Fishburn matrices are not limited to or nonnegative integers . The analytic saddle\u2010point approach we apply, based on a powerful transformation for \u2010series due to Andrews and Jel\u00ednek, is also useful in solving a conjecture of Stoimenow in Vassiliev invariants.<\/jats:p>","DOI":"10.1002\/rsa.21100","type":"journal-article","created":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T07:32:04Z","timestamp":1655191924000},"page":"479-518","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Asymptotics and statistics on Fishburn matrices: Dimension distribution and a conjecture of Stoimenow"],"prefix":"10.1002","volume":"62","author":[{"given":"Hsien\u2010Kuei","family":"Hwang","sequence":"first","affiliation":[{"name":"Institute of Statistical Science Academia Sinica Taipei Taiwan"}]},{"given":"Emma Yu","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences Xiamen University Xiamen People's Republic of China"},{"name":"Institute f\u00fcr Diskrete Mathematik und Geometrie Techische Universit\u00e4t Wien Vienna Austria"}]},{"given":"Michael J.","family":"Schlosser","sequence":"additional","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik Universit\u00e4t Wien Vienna Austria"}]}],"member":"311","published-online":{"date-parts":[[2022,6,14]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(76)90054-6"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2014.01.003"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/1016082"},{"key":"e_1_2_8_5_1","volume-title":"Probability and measure","author":"Billingsley P.","year":"1995"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.37236\/5999"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2009.12.007"},{"key":"e_1_2_8_8_1","unstructured":"G.BrightwellandM. 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