{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:33:43Z","timestamp":1750307623449,"version":"3.41.0"},"reference-count":0,"publisher":"Association for Computing Machinery (ACM)","issue":"1-2","license":[{"start":{"date-parts":[[2008,7,25]],"date-time":"2008-07-25T00:00:00Z","timestamp":1216944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2008,7,25]]},"abstract":"<jats:p>Many problems of combinatorial enumeration can be reduced to solving multivariate linear recurrences with constant coefficients in wedge-like domains. We survey some results on existence and uniqueness of solutions to such recurrences, on the algebraic nature of their generating functions, and on the methods for solving the corresponding functional equations, in particular the so-called kernel method. We also present a prototype Mathematica package for for obtaining explicit solutions when these generating functions are algebraic of low degree.<\/jats:p>","DOI":"10.1145\/1394042.1394050","type":"journal-article","created":{"date-parts":[[2008,7,29]],"date-time":"2008-07-29T13:22:19Z","timestamp":1217337739000},"page":"18-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Solving multivariate linear recurrences in wedges (abstract only)"],"prefix":"10.1145","volume":"42","author":[{"given":"Marko","family":"Petkovsek","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Physics, Jadranska, Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2008,7,25]]},"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1394042.1394050","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T12:45:52Z","timestamp":1750250752000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1394042.1394050"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7,25]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2008,7,25]]}},"alternative-id":["10.1145\/1394042.1394050"],"URL":"https:\/\/doi.org\/10.1145\/1394042.1394050","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2008,7,25]]},"assertion":[{"value":"2008-07-25","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}