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Computer programming --- Factorization (Mathematics)

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This textbook is an introduction to the concept of factorization and its application to problems in algebra and number theory. With the minimum of prerequisites, the reader is introduced to the notion of rings, fields, prime elements and unique factorization. The author shows how concepts can be applied to a variety of examples such as factorizing polynomials, finding determinants of matrices and Fermat's 'two-squares theorem'. Based on an undergraduate course given at the University of Sheffield, Dr Sharpe has included numerous examples which demonstrate how frequently these ideas are useful in concrete, rather than abstract, settings. The book also contains many exercises of varying degrees of difficulty together with hints and solutions. Second and third year undergraduates will find this a readable and enjoyable account of a subject lying at the heart of much of mathematics.

Rings (Algebra) --- Factorization (Mathematics)

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In this paper the authors prove the following results (via a unified approach) for all sufficiently large n: (i) [1-factorization conjecture] Suppose that n is even and Dgeq 2lceil n/4ceil -1. Then every D-regular graph G on n vertices has a decomposition into perfect matchings. Equivalently, chi'(G)=D. (ii) [Hamilton decomposition conjecture] Suppose that D ge lfloor n/2 floor . Then every D-regular graph G on n vertices has a decomposition into Hamilton cycles and at most one perfect matching. (iii) [Optimal packings of Hamilton cycles] Suppose that G is a graph on n vertices with minimum degree deltage n/2. Then G contains at least {m reg}_{m even}(n,delta)/2 ge (n-2)/8 edge-disjoint Hamilton cycles. Here {m reg}_{m even}(n,delta) denotes the degree of the largest even-regular spanning subgraph one can guarantee in a graph on n vertices with minimum degree delta. (i) was first explicitly stated by Chetwynd and Hilton. (ii) and the special case delta= lceil n/2 ceil of (iii) answer questions of Nash-Williams from 1970. All of the above bounds are best possible.

Factorization (Mathematics) --- Decomposition (Mathematics)

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Boundary value problems. --- Factorization (Mathematics) --- Invariant imbedding.

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Factorization (Mathematics) --- Decomposition (Mathematics) --- Factorisation --- Décomposition (Mathématiques)