Theory Of Symmetric Lattices PDF Download
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Author | : Fumitomo Maeda |
Publisher | : Springer Science & Business Media |
Total Pages | : 204 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642462480 |
Download Theory of Symmetric Lattices Book in PDF, ePub and Kindle
Of central importance in this book is the concept of modularity in lattices. A lattice is said to be modular if every pair of its elements is a modular pair. The properties of modular lattices have been carefully investigated by numerous mathematicians, including 1. von Neumann who introduced the important study of continuous geometry. Continu ous geometry is a generalization of projective geometry; the latter is atomistic and discrete dimensional while the former may include a continuous dimensional part. Meanwhile there are many non-modular lattices. Among these there exist some lattices wherein modularity is symmetric, that is, if a pair (a,b) is modular then so is (b,a). These lattices are said to be M-sym metric, and their study forms an extension of the theory of modular lattices. An important example of an M-symmetric lattice arises from affine geometry. Here the lattice of affine sets is upper continuous, atomistic, and has the covering property. Such a lattice, called a matroid lattice, can be shown to be M-symmetric. We have a deep theory of parallelism in an affine matroid lattice, a special kind of matroid lattice. Further more we can show that this lattice has a modular extension.
Author | : Shūichirō Maeda |
Publisher | : |
Total Pages | : 596 |
Release | : 1968 |
Genre | : Lattice theory |
ISBN | : |
Download Theory of Symmetric Lattices Book in PDF, ePub and Kindle
Author | : Fumitomo Maeda |
Publisher | : |
Total Pages | : 201 |
Release | : 1970 |
Genre | : |
ISBN | : |
Download Theory of Symmetric Lattices [ Fumitomo Maeda, Suichiro Maeda Book in PDF, ePub and Kindle
Author | : S. Maeda |
Publisher | : |
Total Pages | : 190 |
Release | : 1970 |
Genre | : |
ISBN | : |
Download F. Maeda [and] S. Maeda ;Theory of Symmetric Lattices Book in PDF, ePub and Kindle
Author | : F. Maeda |
Publisher | : |
Total Pages | : 189 |
Release | : 1970 |
Genre | : Symmetry |
ISBN | : |
Download Theory of Symmetry Lattices Book in PDF, ePub and Kindle
Author | : Peter Crawley |
Publisher | : Prentice Hall |
Total Pages | : 216 |
Release | : 1973 |
Genre | : Mathematics |
ISBN | : |
Download Algebraic Theory of Lattices Book in PDF, ePub and Kindle
Author | : Christopher Bradley |
Publisher | : Oxford University Press |
Total Pages | : 758 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0199582580 |
Download The Mathematical Theory of Symmetry in Solids Book in PDF, ePub and Kindle
This classic book gives, in extensive tables, the irreducible representations of the crystallographic point groups and space groups. These are useful in studying the eigenvalues and eigenfunctions of a particle or quasi-particle in a crystalline solid. The theory is extended to the corepresentations of the Shubnikov groups.
Author | : George Grätzer |
Publisher | : Birkhäuser |
Total Pages | : 625 |
Release | : 2016-10-08 |
Genre | : Mathematics |
ISBN | : 3319442368 |
Download Lattice Theory: Special Topics and Applications Book in PDF, ePub and Kindle
George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, in two volumes, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This second volume is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.
Author | : Stephen D. Comer |
Publisher | : Springer |
Total Pages | : 290 |
Release | : 2006-12-08 |
Genre | : Mathematics |
ISBN | : 3540396381 |
Download Universal Algebra and Lattice Theory Book in PDF, ePub and Kindle
Author | : Lynne M. Butler |
Publisher | : American Mathematical Soc. |
Total Pages | : 176 |
Release | : 1994-12-12 |
Genre | : Mathematics |
ISBN | : 9780821862629 |
Download Subgroup Lattices and Symmetric Functions Book in PDF, ePub and Kindle
This work presents foundational research on two approaches to studying subgroup lattices of finite abelian $p$-groups. The first approach is linear algebraic in nature and generalizes Knuth's study of subspace lattices. This approach yields a combinatorial interpretation of the Betti polynomials of these Cohen-Macaulay posets. The second approach, which employs Hall-Littlewood symmetric functions, exploits properties of Kostka polynomials to obtain enumerative results such as rank-unimodality. Butler completes Lascoux and Schutzenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.