[{"abstract":[{"lang":"eng"}],"extern":"1","user_id":"93826","keyword":[],"publication":"LMS Journal of Computation and Mathematics","author":[{"last_name":"Lorch","first_name":"David"},{"first_name":"Markus","last_name":"Kirschmer","id":"82258"}],"date_created":"2023-03-07T08:34:28Z","status":"public","volume":16,"_id":"42796","intvolume":" 16","page":"172-186","uri_base":"https://ris.uni-paderborn.de","type":"journal_article","citation":{"chicago":"Lorch, David, and Markus Kirschmer. “Single-Class Genera of Positive Integral Lattices.” LMS Journal of Computation and Mathematics 16 (2013): 172–86. https://doi.org/10.1112/s1461157013000107.","apa":"Lorch, D., & Kirschmer, M. (2013). Single-class genera of positive integral lattices. LMS Journal of Computation and Mathematics, 16, 172–186. https://doi.org/10.1112/s1461157013000107","bibtex":"@article{Lorch_Kirschmer_2013, title={Single-class genera of positive integral lattices}, volume={16}, DOI={10.1112/s1461157013000107}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Lorch, David and Kirschmer, Markus}, year={2013}, pages={172–186} }","mla":"Lorch, David, and Markus Kirschmer. “Single-Class Genera of Positive Integral Lattices.” LMS Journal of Computation and Mathematics, vol. 16, Wiley, 2013, pp. 172–86, doi:10.1112/s1461157013000107.","short":"D. Lorch, M. Kirschmer, LMS Journal of Computation and Mathematics 16 (2013) 172–186.","ieee":"D. Lorch and M. Kirschmer, “Single-class genera of positive integral lattices,” LMS Journal of Computation and Mathematics, vol. 16, pp. 172–186, 2013, doi: 10.1112/s1461157013000107."},"dc":{"identifier":["https://ris.uni-paderborn.de/record/42796"],"date":["2013"],"title":["Single-class genera of positive integral lattices"],"publisher":["Wiley"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1112/s1461157013000107","info:eu-repo/semantics/altIdentifier/issn/1461-1570"],"description":["We give an enumeration of all positive definite primitive Z-lattices in dimension n ≥ 3 whose genus consists of a single isometry class. This is achieved by using bounds obtained from the Smith–Minkowski–Siegel mass formula to computationally construct the square-free determinant lattices with this property, and then repeatedly calculating pre-images under a mapping first introduced by G. L. Watson.\r\n\r\nWe hereby complete the classification of single-class genera in dimensions 4 and 5 and correct some mistakes in Watson’s classifications in other dimensions. A list of all single-class primitive Z-lattices has been compiled and incorporated into the Catalogue of Lattices."],"source":["Lorch D, Kirschmer M. Single-class genera of positive integral lattices. LMS Journal of Computation and Mathematics. 2013;16:172-186. doi:10.1112/s1461157013000107"],"creator":["Lorch, David","Kirschmer, Markus"],"rights":["info:eu-repo/semantics/closedAccess"],"subject":["Computational Theory and Mathematics","General Mathematics"],"language":["eng"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"]},"department":[{"tree":[{"_id":"99"},{"_id":"10"},{"_id":"34"},{"_id":"44"},{"_id":"43"}],"_id":"102"}],"dini_type":"doc-type:article","publication_status":"published","publication_identifier":{"issn":[]},"date_updated":"2023-04-04T07:57:04Z","creator":{"login":"ckoerber","id":"93826"},"language":[{}]}]