{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:05:20Z","timestamp":1787321120587,"version":"build-2736575974"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["1970\/18"],"award-info":[{"award-number":["1970\/18"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We consider a sequence of four variable polynomials by refining Stieltjes's continued fraction for Eulerian polynomials. Using combinatorial theory of Jacobi-type continued fractions and bijections, we derive various combinatorial interpretations in terms of permutation statistics for these polynomials, which include special kinds of descents and excedances in a recent paper of Baril and Kirgizov. As a byproduct, we derive several equidistribution results for permutation statistics, which enables us to confirm and strengthen a recent conjecture of Vajnovszki and also to obtain several companion permutation statistics for two bistatistics in a conjecture of Baril and Kirgizov.<\/jats:p>","DOI":"10.1137\/21m1414541","type":"journal-article","created":{"date-parts":[[2021,11,30]],"date-time":"2021-11-30T11:05:14Z","timestamp":1638270314000},"page":"2858-2879","source":"Crossref","is-referenced-by-count":1,"title":["Equidistributions around Special Kinds of Descents and Excedances"],"prefix":"10.1137","volume":"35","author":[{"given":"Bin","family":"Han","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianxi","family":"Mao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiang","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,11,30]]},"reference":[{"key":"atypb1","first-page":"R19","volume":"1","author":"Baril J.-L.","year":"2021","journal-title":"Enumer. Combin. Appl."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/8330"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2006.12.010"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1006\/aama.1996.0506"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2006.01.006"},{"key":"atypb6","first-page":"11","volume":"19","author":"Elizalde S.","year":"2017","journal-title":"Discrete Math. Theor. Comput. Sci."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(80)90050-3"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"D. Foata and M. P. Sch\u00fctzenberger,\n                      Th\u00e9orie G\u00e9om\u00e9trique des Polyn\u00f4mes Eul\u00e9riens\n                      , Lecture Notes in Math. 138, Springer-Verlag, Berlin, 1970.","DOI":"10.1007\/BFb0060799"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01237393"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1002\/sapm199083131"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(79)90182-1"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/20M1340538"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2020.102092"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2020.102149"},{"key":"atypb15","first-page":"B49e","volume":"49","author":"Ksavrelof G.","year":"2002","journal-title":"S\u00e9m. Lothar. Combin."},{"key":"atypb16","unstructured":"S.M. Ma, J. Ma, J. Yeh, and Y.N. Yeh,\n                      Excedance-Type Polynomials and Gamma-Positivity\n                      , preprint,https:\/\/arxiv.org\/abs\/2102.00899, 2021."},{"key":"atypb17","unstructured":"P. A. MacMahon,\n                      Combinatory Analysis\n                      , Vol. I, II (bound in one volume), reprint of An Introduction to Combinatory Analysis (1920) and Combinatory Analysis, Vol. I, II (1915, 1916), Dover Phoenix Editions, Dover, Mineola, NY, 2004."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2021.112337"},{"key":"atypb19","doi-asserted-by":"crossref","unstructured":"T. K. Petersen,\n                      Eulerian Numbers\n                      , Birkh\u00e4user Adv. Texts Basler Lehrb\u00fccher, Birkh\u00e4user\/Springer, New York, 2015.","DOI":"10.1007\/978-1-4939-3091-3"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/0604046"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2010.04.003"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2011.08.005"},{"key":"atypb24","unstructured":"A. D. Sokal and J. Zeng,\n                      Some Multivariate Master Polynomials for Permutations, Set Partitions, and Perfect Matchings, and Their Continued Fractions\n                      , preprint,https:\/\/arxiv.org\/abs\/2003.08192, 2020."},{"key":"atypb25","doi-asserted-by":"crossref","unstructured":"R. P. Stanley,\n                      Enumerative Combinatorics, Vol.\n                      1, Cambridge University Press, Cambridge, UK, 1997.","DOI":"10.1017\/CBO9780511805967"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.1993.1041"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/21M1414541","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:06:57Z","timestamp":1787317617000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1414541"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/21M1414541"],"URL":"https:\/\/doi.org\/10.1137\/21m1414541","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}