{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T05:12:02Z","timestamp":1648962722697},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p> This paper closes an algorithmic problem of summing a set of mutual recurrence relations with constant coefficients. Given an order d system of the form [Formula: see text], where A, G : \u2115 \u2192 K<jats:sup>m<\/jats:sup> and M<jats:sub>1<\/jats:sub>,\u2026, M<jats:sub>d<\/jats:sub> \u2208 M<jats:sub>m<\/jats:sub>(K) for some field K and natural number m, this algorithm computes the sum [Formula: see text] as a K-linear combination of A(n),\u2026, A(n - d), the initial conditions and sums of the inhomogeneous term G(n). The runtime of this algorithm is shown to be polynomial in m and d. <\/jats:p>","DOI":"10.1142\/s1793830912500164","type":"journal-article","created":{"date-parts":[[2012,6,19]],"date-time":"2012-06-19T10:55:53Z","timestamp":1340103353000},"page":"1250016","source":"Crossref","is-referenced-by-count":0,"title":["AN EFFICIENT ALGORITHM FOR DERIVING SUMMATION IDENTITIES FROM MUTUAL RECURRENCES"],"prefix":"10.1142","volume":"04","author":[{"given":"BERKELEY R.","family":"CHURCHILL","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of California Santa Barbara, Santa Barbara, California 93117, USA"}]},{"given":"EDMUND A.","family":"LAMAGNA","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Statistics, University of Rhode Island, Kingston, Rhode Island 02881, USA"}]}],"member":"219","published-online":{"date-parts":[[2012,6,21]]},"reference":[{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(99)00259-9"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(08)80013-2"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.75.1.40"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-06-03994-8"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1145\/322248.322255"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2008.03.002"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2004.07.009"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(90)90120-7"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830912500164","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:42:06Z","timestamp":1565116926000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830912500164"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6]]},"references-count":8,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,6,21]]},"published-print":{"date-parts":[[2012,6]]}},"alternative-id":["10.1142\/S1793830912500164"],"URL":"https:\/\/doi.org\/10.1142\/s1793830912500164","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6]]}}}