Factoring Groups into Subsets
Seiten
2017
CRC Press (Verlag)
978-1-138-40171-6 (ISBN)
CRC Press (Verlag)
978-1-138-40171-6 (ISBN)
Focusing mainly on cyclic groups, this book explores the factorization theory of abelian groups. It shows how to construct fresh factorizations from old ones. It discusses non periodic and periodic factorizations, quasi periodicity, and the factoring of periodic subsets.
Decomposing an abelian group into a direct sum of its subsets leads to results that can be applied to a variety of areas, such as number theory, geometry of tilings, coding theory, cryptography, graph theory, and Fourier analysis. Focusing mainly on cyclic groups, Factoring Groups into Subsets explores the factorization theory of abelian groups.
The book first shows how to construct new factorizations from old ones. The authors then discuss nonperiodic and periodic factorizations, quasiperiodicity, and the factoring of periodic subsets. They also examine how tiling plays an important role in number theory. The next several chapters cover factorizations of infinite abelian groups; combinatorics, such as Ramsey numbers, Latin squares, and complex Hadamard matrices; and connections with codes, including variable length codes, error correcting codes, and integer codes. The final chapter deals with several classical problems of Fuchs.
Encompassing many of the main areas of the factorization theory, this book explores problems in which the underlying factored group is cyclic.
Decomposing an abelian group into a direct sum of its subsets leads to results that can be applied to a variety of areas, such as number theory, geometry of tilings, coding theory, cryptography, graph theory, and Fourier analysis. Focusing mainly on cyclic groups, Factoring Groups into Subsets explores the factorization theory of abelian groups.
The book first shows how to construct new factorizations from old ones. The authors then discuss nonperiodic and periodic factorizations, quasiperiodicity, and the factoring of periodic subsets. They also examine how tiling plays an important role in number theory. The next several chapters cover factorizations of infinite abelian groups; combinatorics, such as Ramsey numbers, Latin squares, and complex Hadamard matrices; and connections with codes, including variable length codes, error correcting codes, and integer codes. The final chapter deals with several classical problems of Fuchs.
Encompassing many of the main areas of the factorization theory, this book explores problems in which the underlying factored group is cyclic.
Sandor Szabo, Arthur D. Sands
Introduction. New Factorizations from Old Ones. Nonperiodic Factorizations. Periodic Factorizations. Various Factorizations. Factoring by Many Factors. Group of Integers. Infinite Groups. Combinatorics. Codes. Some Classical Problems. References. Index.
| Erscheinungsdatum | 28.11.2017 |
|---|---|
| Reihe/Serie | Lecture Notes in Pure and Applied Mathematics |
| Verlagsort | London |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 453 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| ISBN-10 | 1-138-40171-4 / 1138401714 |
| ISBN-13 | 978-1-138-40171-6 / 9781138401716 |
| Zustand | Neuware |
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