{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T01:40:01Z","timestamp":1723081201158},"reference-count":0,"publisher":"Wiley","issue":"32","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>We study birational monomial transformations of the form , where <jats:italic>\u03f5<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>\u03f5<\/jats:italic><jats:sub>2<\/jats:sub> \u2208 {\u22121, 1}. These transformations form a group. We describe this group in terms of generators and relations and, for every such transformation <jats:italic>\u03c6<\/jats:italic>, we prove a formula, which represents the transformation <jats:italic>\u03c6<\/jats:italic> as a product of generators of the group. To prove this formula, we use birationally equivalent polynomials <jats:italic>A<\/jats:italic><jats:italic>x<\/jats:italic> + <jats:italic>B<\/jats:italic><jats:italic>y<\/jats:italic> + <jats:italic>C<\/jats:italic> and <jats:italic>A<\/jats:italic><jats:italic>x<\/jats:italic><jats:sup><jats:italic>p<\/jats:italic><\/jats:sup> + <jats:italic>B<\/jats:italic><jats:italic>y<\/jats:italic><jats:sup><jats:italic>q<\/jats:italic><\/jats:sup> + <jats:italic>C<\/jats:italic><jats:italic>x<\/jats:italic><jats:sup><jats:italic>r<\/jats:italic><\/jats:sup><jats:italic>y<\/jats:italic><jats:sup><jats:italic>s<\/jats:italic><\/jats:sup>. If <jats:italic>\u03c6<\/jats:italic> is the transformation which carries one polynomial onto another, then the integral powers of generators in the product, which represents the transformation <jats:italic>\u03c6<\/jats:italic>, can be calculated by the expansion of <jats:italic>p<\/jats:italic>\/<jats:italic>q<\/jats:italic> in the continued fraction.<\/jats:p>","DOI":"10.1155\/s0161171204306514","type":"journal-article","created":{"date-parts":[[2004,7,21]],"date-time":"2004-07-21T05:51:24Z","timestamp":1090389084000},"page":"1671-1677","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On birational monomial transformations of plane"],"prefix":"10.1155","volume":"2004","author":[{"given":"Anatoly B.","family":"Korchagin","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,7,20]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/438417.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171204306514","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T00:50:52Z","timestamp":1723078252000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171204306514"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":0,"journal-issue":{"issue":"32","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1155\/S0161171204306514"],"URL":"https:\/\/doi.org\/10.1155\/s0161171204306514","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2004,1]]},"assertion":[{"value":"2003-06-20","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2004-07-20","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}