Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Introduction to algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Spherical designs and finite group representations (some results of E. Bannai)
European Journal of Combinatorics - Special issue on algebraic combinatorics: in memory of J.J. Seidel
Construction of new extremal unimodular lattices
European Journal of Combinatorics - Special issue on arithmétique et combinatoire
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We derive a mass formula for n-dimensional unimodular lattices having any prescribed root system. We use Katsurada's formula for the Fourier coefficients of Siegel Eisenstein series to compute these masses for all root systems of even unimodular 32-dimensional lattices and odd unimodular lattices of dimension n ≤ 30. In particular, we find the mass of even unimodular 32- dimensional lattices with no roots, and the mass of odd unimodular lattices with no roots in dimension n ≤ 30, verifying Bacher and Venkov's enumerations in dimensions 27 and 28. We also compute better lower bounds on the number of inequivalent unimodular lattices in dimensions 26 to 30 than those afforded by the Minkowski-Siegel mass constants.