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ISBN: 0824773314 9780824773311 Year: 1985 Publisher: New York (N.Y.): Dekker,
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Year: 1970 Publisher: Berlin,New York : Springer-Verlag,
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ISBN: 0198503695 Year: 1988 Publisher: Oxford : New York : Clarendon Press Oxford University Press,
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ISBN: 1139886568 0511960905 1107103096 0521118840 1107088704 0511665571 1107094933 1107091640 9781107088702 9780511665578 9781107094932 9780521461054 0521461057 9780521118842 Year: 1999 Volume: 73 Publisher: Cambridge Cambridge University Press
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In Semimodular Lattices: Theory and Applications Manfred Stern uses successive generalizations of distributive and modular lattices to outline the development of semimodular lattices from Boolean algebras. He focuses on the important theory of semimodularity, its many ramifications, and its applications in discrete mathematics, combinatorics, and algebra. The book surveys and analyzes Garrett Birkhoff's concept of semimodularity and the various related concepts in lattice theory, and it presents theoretical results as well as applications in discrete mathematics group theory and universal algebra. The author also deals with lattices that are 'close' to semimodularity or can be combined with semimodularity, e.g. supersolvable, admissible, consistent, strong, and balanced lattices. Researchers in lattice theory, discrete mathematics, combinatorics, and algebra will find this book invaluable.
Semimodular lattices. --- Lattices, Semimodular --- Semi-Dedekind lattices --- Semi-modular lattices --- Modular lattices --- Semimodular lattices
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ISBN: 1000020381 3866445849 Year: 2010 Publisher: KIT Scientific Publishing
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The aim of this work is to study Schmutz Schaller's conjecture that in dimensions 2 to 8 the lattices with the best sphere packings have maximal lengths. This means that the distinct norms which occur in these lattices are greater than those of any other lattice in the same dimension with the same covolume. Although the statement holds asymptotically we explicitly present a counter-example. However, it seems that there is nothing but this exception.
Lattices --- Geodesics --- Quadratic Forms
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Year: 1964 Publisher: Edinburgh: Oliver and Boyd,
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Year: 1968 Publisher: Berlin : Springer,
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ISBN: 0821824910 Year: 1990 Publisher: Providence (R.I.): American Mathematical Society
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