article published David Lorch author Markus Kirschmer author 82258 102 department 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. We 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. Wiley2013 eng Computational Theory and MathematicsGeneral Mathematics 1461-157010.1112/s1461157013000107 16172-186 yes Lorch, David, and Markus Kirschmer. “Single-Class Genera of Positive Integral Lattices.” <i>LMS Journal of Computation and Mathematics</i>, vol. 16, Wiley, 2013, pp. 172–86, doi:<a href="https://doi.org/10.1112/s1461157013000107">10.1112/s1461157013000107</a>. Lorch D, Kirschmer M. Single-class genera of positive integral lattices. <i>LMS Journal of Computation and Mathematics</i>. 2013;16:172-186. doi:<a href="https://doi.org/10.1112/s1461157013000107">10.1112/s1461157013000107</a> @article{Lorch_Kirschmer_2013, title={Single-class genera of positive integral lattices}, volume={16}, DOI={<a href="https://doi.org/10.1112/s1461157013000107">10.1112/s1461157013000107</a>}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Lorch, David and Kirschmer, Markus}, year={2013}, pages={172–186} } Lorch, D., &#38; Kirschmer, M. (2013). Single-class genera of positive integral lattices. <i>LMS Journal of Computation and Mathematics</i>, <i>16</i>, 172–186. <a href="https://doi.org/10.1112/s1461157013000107">https://doi.org/10.1112/s1461157013000107</a> D. Lorch and M. Kirschmer, “Single-class genera of positive integral lattices,” <i>LMS Journal of Computation and Mathematics</i>, vol. 16, pp. 172–186, 2013, doi: <a href="https://doi.org/10.1112/s1461157013000107">10.1112/s1461157013000107</a>. Lorch, David, and Markus Kirschmer. “Single-Class Genera of Positive Integral Lattices.” <i>LMS Journal of Computation and Mathematics</i> 16 (2013): 172–86. <a href="https://doi.org/10.1112/s1461157013000107">https://doi.org/10.1112/s1461157013000107</a>. D. Lorch, M. Kirschmer, LMS Journal of Computation and Mathematics 16 (2013) 172–186. 427962023-03-07T08:34:28Z2023-04-04T07:57:04Z