{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T09:49:13Z","timestamp":1764841753206,"version":"3.40.5"},"reference-count":8,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11261032","1010RJZA049"],"award-info":[{"award-number":["11261032","1010RJZA049"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004775","name":"Natural Science Foundation of Gansu Province","doi-asserted-by":"publisher","award":["11261032","1010RJZA049"],"award-info":[{"award-number":["11261032","1010RJZA049"]}],"id":[{"id":"10.13039\/501100004775","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>By presenting Riordan matrix as a triangle, the central coefficients are entries in the central column. Starting at the central column, the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>r<\/mml:mi><\/mml:mrow><\/mml:math>-shifted central coefficients are entries in column<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>r<\/mml:mi><\/mml:mrow><\/mml:math>of the right part of the triangle. This paper aims to characterize the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>r<\/mml:mi><\/mml:mrow><\/mml:math>-shifted central coefficients of Riordan matrices. Here we will concentrate on four elements of the subgroups of the Riordan group, that is, the Bell subgroup, the associated subgroup, the derivative subgroup, and the hitting time subgroup. Some examples are presented to show how we deduce the generating functions for interesting sequences by using different means of calculating these<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>r<\/mml:mi><\/mml:mrow><\/mml:math>-shifted central coefficients. Besides, we make some extensions in the Bell subgroup.<\/jats:p>","DOI":"10.1155\/2014\/848374","type":"journal-article","created":{"date-parts":[[2014,4,3]],"date-time":"2014-04-03T17:09:44Z","timestamp":1396544984000},"page":"1-8","source":"Crossref","is-referenced-by-count":2,"title":["On the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>r<\/mml:mi><\/mml:mrow><\/mml:math>-Shifted Central Coefficients of Riordan Matrices"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4932-8464","authenticated-orcid":true,"given":"Sai-nan","family":"Zheng","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9314-346X","authenticated-orcid":true,"given":"Sheng-liang","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"issue":"4","key":"1","first-page":"Article 11.4.3","volume":"14","year":"2011","journal-title":"Journal of Integer Sequences"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(91)90088-E"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(03)00227-5"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(99)00166-3"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(78)90063-8"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.11.021"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-006-9077-7"},{"year":"1989","key":"11"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/848374.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/848374.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/848374.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,29]],"date-time":"2016-07-29T06:06:34Z","timestamp":1469772394000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/848374\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":8,"alternative-id":["848374","848374"],"URL":"https:\/\/doi.org\/10.1155\/2014\/848374","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}