{"id":160,"date":"2017-01-17T12:34:48","date_gmt":"2017-01-17T12:34:48","guid":{"rendered":"http:\/\/users.utu.fi\/hietarin\/?page_id=160"},"modified":"2017-01-17T13:51:11","modified_gmt":"2017-01-17T13:51:11","slug":"yang-baxter-equations","status":"publish","type":"page","link":"https:\/\/users.utu.fi\/hietarin\/home\/yang-baxter-equations\/","title":{"rendered":"Yang-Baxter and other simplex equations"},"content":{"rendered":"<h3>Set theoretical solutions<\/h3>\n<ul>\n<li>J. Hietarinta: <em>Permutation type solutions to the Yang-Baxter and\u00a0other n-simplex equations<\/em>, <a href=\"http:\/\/dx.doi.org\/10.1088\/0305-4470\/30\/13\/024\">J. Phys. A: Math. Gen. <b> 30<\/b>, 4757-4771 (1997).<\/a><\/li>\n<\/ul>\n<h3>Tetrahedron equations<\/h3>\n<ul>\n<li>J. Hietarinta and F. Nijhoff: <em>The eight tetrahedron equations<\/em>, <a href=\"http:\/\/dx.doi.org\/10.1063\/1.532055\">J. Math. Phys. <b> 38<\/b>, 3603-3615 (1997).<\/a><\/li>\n<li>J. Hietarinta: <em>Labelling schemes for tetrahedron equations and dualities between them<\/em>,<a href=\"http:\/\/dx.doi.org\/10.1088\/0305-4470\/27\/17\/010\"> J. Phys. A: Math. Gen. <b> 27<\/b>, 5727-5748 (1994).<\/a><\/li>\n<li>J. Hietarinta: <em>Some constant solutions to Zamolodchikov&#8217;s tetrahedron equations<\/em>,<a href=\"http:\/\/dx.doi.org\/10.1088\/0305-4470\/26\/1\/003\"> J. Phys. A: Math. Gen. <b> 26<\/b>, L9-L15 (1993).<\/a><\/li>\n<\/ul>\n<h3>\u00a0Yang-Baxter equations<\/h3>\n<ul>\n<li>J. Hietarinta: <em>The upper triangular solutions to the three-state constant quantum Yang-Baxter equation<\/em>,<a href=\"http:\/\/dx.doi.org\/10.1088\/0305-4470\/26\/23\/044\"> J. Phys. A: Math. Gen. <b> 26<\/b>,7077-7095 (1993).<\/a><\/li>\n<li>J. Hietarinta: <em>Solving the two-dimensional constant quantum Yang-Baxter equation<\/em>,<a href=\"http:\/\/dx.doi.org\/10.1063\/1.530185\"> J. Math. Phys. <b> 34<\/b>, 1725-1756 (1993).<\/a><\/li>\n<li>J. Hietarinta: <em>All solutions to the constant quantum Yang-Baxter equation in two dimensions<\/em>, <a href=\"http:\/\/dx.doi.org\/10.1016\/0375-9601(92)90044-M\">Phys. Lett. A <b>165<\/b>, 245-251 (1992). <\/a><\/li>\n<li>J. Hietarinta: <em> The complete solution to the constant quantum Yang-Baxter equation in two dimensions<\/em>, in <a href=\"http:\/\/www.springer.com\/physics\/book\/978-0-7923-2457-7\">&#8220;Applications of Analytic and Geometric Methods to Nonlinear Differential Equation&#8221;<\/a>, ed.<br \/>\nP. Clarkson, (Kluwer, 1993), pp. 149-154.<\/li>\n<li>J. Hietarinta: <em>Solving huge sets of nonlinear equations<\/em>, in &#8220;Proceedings of the Helsinki Workshop on Symbolic and Numeric Computation, 1993&#8221;, eds. H. Apiola, M. Laine and E. Valkeila, (Rolf Nevanlinna Institute, 1994), Research Reports B10, pp. 139-148.<\/li>\n<li>J. Hietarinta: <em>All solutions to the constant quantum Yang-Baxter equation in 2-dimension<\/em>, in the proceedings of &#8220;XIX International Colloquium on Group Theoretical Methods in Physics&#8221;, eds. M.A. del Olmo, M. Santander and J. Mateos-Guilarte, (CIEMAT, 1993), Vol I, pp. 241-244.<\/li>\n<li>J. Hietarinta: <em> Solving the constant quantum Yang-Baxter equation in 2 dimensions with massive use of factorizing Gr\u00f6bner basis computations<\/em>, in <a href=\"http:\/\/doi.acm.org\/10.1145\/143242.143351\">&#8220;Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC&#8217;92&#8221;<\/a>, ed. P.S. Wang, (ACM Press, 1992), pp. 350-357.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Set theoretical solutions J. Hietarinta: Permutation type solutions to the Yang-Baxter and\u00a0other n-simplex equations, J. Phys. A: Math. Gen. 30, 4757-4771 (1997). Tetrahedron equations J. Hietarinta and F. Nijhoff: The eight tetrahedron equations, J. Math. Phys. 38, 3603-3615 (1997). J. Hietarinta: Labelling schemes for tetrahedron equations and dualities between them, J. Phys. A: Math. Gen. &hellip; <a href=\"https:\/\/users.utu.fi\/hietarin\/home\/yang-baxter-equations\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Yang-Baxter and other simplex equations&#8221;<\/span><\/a><\/p>\n","protected":false},"author":178,"featured_media":0,"parent":43,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-160","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/users.utu.fi\/hietarin\/wp-json\/wp\/v2\/pages\/160","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/users.utu.fi\/hietarin\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/users.utu.fi\/hietarin\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/users.utu.fi\/hietarin\/wp-json\/wp\/v2\/users\/178"}],"replies":[{"embeddable":true,"href":"https:\/\/users.utu.fi\/hietarin\/wp-json\/wp\/v2\/comments?post=160"}],"version-history":[{"count":3,"href":"https:\/\/users.utu.fi\/hietarin\/wp-json\/wp\/v2\/pages\/160\/revisions"}],"predecessor-version":[{"id":229,"href":"https:\/\/users.utu.fi\/hietarin\/wp-json\/wp\/v2\/pages\/160\/revisions\/229"}],"up":[{"embeddable":true,"href":"https:\/\/users.utu.fi\/hietarin\/wp-json\/wp\/v2\/pages\/43"}],"wp:attachment":[{"href":"https:\/\/users.utu.fi\/hietarin\/wp-json\/wp\/v2\/media?parent=160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}