This series is devoted to the publication of high-level monographs which cover the whole spectrum of current discrete mathematics and its applications in various fields. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of discrete mathematics. Contributions which are on the borderline of discrete mathematics and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.
The existence of lattices with trivial automorphism group was shown by O'Meara, who gave an algorithm to construct such a lattice starting from any given lattice. In this process, the discriminants of the lattices increase in each step. Biermann proved the existence of a lattice with trivial automorphism group in every genus of positive definite integral lattices of any dimension with sufficiently large discriminant. In his proof the fact that the discriminant is very large is crucial. We are, instead, interested in lattices with small discriminant.
Algebraic combinatorics is the study of combinatorial objects as an extension of the study of finite permutation groups, or, in other words, group theory without groups. In the spirit of Delsarte's theory, this book studies combinatorial objects such as graphs, codes, designs, etc. in the general framework of association schemes, providing a comprehensive overview of the theory as well as pointing out to extensions.
The existence of lattices with trivial automorphism group was shown by O'Meara, who gave an algorithm to construct such a lattice starting from any given lattice. In this process, the discriminants of the lattices increase in each step. Biermann proved the existence of a lattice with trivial automorphism group in every genus of positive definite integral lattices of any dimension with sufficiently large discriminant. In his proof the fact that the discriminant is very large is crucial. We are, instead, interested in lattices with small discriminant.
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