Row polynomial matrices of Riordan arrays

Let R=[rn,k]n,k≥0 be a Riordan array. Define the row polynomials Rn(q)=∑k=0nrn,kqk and the row polynomial matrix R(q)=[rn,k(q)]n,k≥0 by rn,k(q)=∑j=knrn,jqj−k. Then R(q) is also a Riordan array with the Rn(q) located on the leftmost column of R(q). In this paper we investigate combinatorial propertie...

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Veröffentlicht in:	Linear algebra and its applications 2017-06, Vol.522, p.1-14
Hauptverfasser:	Mu, Lili, Mao, Jianxi, Wang, Yi
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Sprache:	eng
Schlagworte:	Arrays Combinatorial analysis Combinatorics Convexity Linear algebra Linear equations Log-convexity Matrix Polynomial matrices Polynomials Riordan array Total positivity
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description	Let R=[rn,k]n,k≥0 be a Riordan array. Define the row polynomials Rn(q)=∑k=0nrn,kqk and the row polynomial matrix R(q)=[rn,k(q)]n,k≥0 by rn,k(q)=∑j=knrn,jqj−k. Then R(q) is also a Riordan array with the Rn(q) located on the leftmost column of R(q). In this paper we investigate combinatorial properties of the matrix R(q) and the sequence (Rn(q))n≥0, including their characterizations, the q-total positivity of R(q) and the q-log-convexity of (Rn(q))n≥0.
doi_str_mv	10.1016/j.laa.2017.02.006
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Define the row polynomials Rn(q)=∑k=0nrn,kqk and the row polynomial matrix R(q)=[rn,k(q)]n,k≥0 by rn,k(q)=∑j=knrn,jqj−k. Then R(q) is also a Riordan array with the Rn(q) located on the leftmost column of R(q). In this paper we investigate combinatorial properties of the matrix R(q) and the sequence (Rn(q))n≥0, including their characterizations, the q-total positivity of R(q) and the q-log-convexity of (Rn(q))n≥0.</description><identifier>ISSN: 0024-3795</identifier><identifier>EISSN: 1873-1856</identifier><identifier>DOI: 10.1016/j.laa.2017.02.006</identifier><language>eng</language><publisher>Amsterdam: Elsevier Inc</publisher><subject>Arrays ; Combinatorial analysis ; Combinatorics ; Convexity ; Linear algebra ; Linear equations ; Log-convexity ; Matrix ; Polynomial matrices ; Polynomials ; Riordan array ; Total positivity</subject><ispartof>Linear algebra and its applications, 2017-06, Vol.522, p.1-14</ispartof><rights>2017 Elsevier Inc.</rights><rights>Copyright American Elsevier Company, Inc. 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Define the row polynomials Rn(q)=∑k=0nrn,kqk and the row polynomial matrix R(q)=[rn,k(q)]n,k≥0 by rn,k(q)=∑j=knrn,jqj−k. Then R(q) is also a Riordan array with the Rn(q) located on the leftmost column of R(q). In this paper we investigate combinatorial properties of the matrix R(q) and the sequence (Rn(q))n≥0, including their characterizations, the q-total positivity of R(q) and the q-log-convexity of (Rn(q))n≥0.</description><subject>Arrays</subject><subject>Combinatorial analysis</subject><subject>Combinatorics</subject><subject>Convexity</subject><subject>Linear algebra</subject><subject>Linear equations</subject><subject>Log-convexity</subject><subject>Matrix</subject><subject>Polynomial matrices</subject><subject>Polynomials</subject><subject>Riordan array</subject><subject>Total positivity</subject><issn>0024-3795</issn><issn>1873-1856</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMoWFd_gLeCJw-tk6-mwZMsfsGCsOg5xDSBlLapSVfZf2-W9SxzmMv7vDM8CF1jqDHg5q6vB61rAljUQGqA5gQVuBW0wi1vTlEBQFhFheTn6CKlHgCYAFKg2234Kecw7Kcwej2Uo16iNzaVwZVbH2Knp1LHqPfpEp05PSR79bdX6OPp8X39Um3enl_XD5vKUMKXijAiMWsxMIOZZLwxbcMlFZQJShyTvLOf1uURHdiWSWmMxZRQYJS7jju6QjfH3jmGr51Ni-rDLk75pCLQSkEpbkhO4WPKxJBStE7N0Y867hUGdTCiepWNqIMRBURlI5m5PzI2v__tbVTJeDsZ2_lozaK64P-hfwFwGmZT</recordid><startdate>20170601</startdate><enddate>20170601</enddate><creator>Mu, Lili</creator><creator>Mao, Jianxi</creator><creator>Wang, Yi</creator><general>Elsevier Inc</general><general>American Elsevier Company, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0003-2500-2275</orcidid></search><sort><creationdate>20170601</creationdate><title>Row polynomial matrices of Riordan arrays</title><author>Mu, Lili ; Mao, Jianxi ; Wang, Yi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-2429148104c149456c86593734732f495debefefe7d0e8499cce13230435fd5f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Arrays</topic><topic>Combinatorial analysis</topic><topic>Combinatorics</topic><topic>Convexity</topic><topic>Linear algebra</topic><topic>Linear equations</topic><topic>Log-convexity</topic><topic>Matrix</topic><topic>Polynomial matrices</topic><topic>Polynomials</topic><topic>Riordan array</topic><topic>Total positivity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mu, Lili</creatorcontrib><creatorcontrib>Mao, Jianxi</creatorcontrib><creatorcontrib>Wang, Yi</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Linear algebra and its applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mu, Lili</au><au>Mao, Jianxi</au><au>Wang, Yi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Row polynomial matrices of Riordan arrays</atitle><jtitle>Linear algebra and its applications</jtitle><date>2017-06-01</date><risdate>2017</risdate><volume>522</volume><spage>1</spage><epage>14</epage><pages>1-14</pages><issn>0024-3795</issn><eissn>1873-1856</eissn><abstract>Let R=[rn,k]n,k≥0 be a Riordan array. 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subjects	Arrays Combinatorial analysis Combinatorics Convexity Linear algebra Linear equations Log-convexity Matrix Polynomial matrices Polynomials Riordan array Total positivity
title	Row polynomial matrices of Riordan arrays
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