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Computations and Combinatorics in Commutative Algebra: EACA School, Valladolid 2013 1st ed. 2017 [Pehme köide]

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  • Formaat: Paperback / softback, 127 pages, kõrgus x laius: 235x155 mm, kaal: 2234 g, 16 Illustrations, color; 9 Illustrations, black and white; VIII, 127 p. 25 illus., 16 illus. in color., 1 Paperback / softback
  • Sari: Lecture Notes in Mathematics 2176
  • Ilmumisaeg: 15-Mar-2017
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319513184
  • ISBN-13: 9783319513188
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Computations and Combinatorics in Commutative Algebra: EACA School, Valladolid 2013 1st ed. 2017Suurem pilt
  • Formaat: Paperback / softback, 127 pages, kõrgus x laius: 235x155 mm, kaal: 2234 g, 16 Illustrations, color; 9 Illustrations, black and white; VIII, 127 p. 25 illus., 16 illus. in color., 1 Paperback / softback
  • Sari: Lecture Notes in Mathematics 2176
  • Ilmumisaeg: 15-Mar-2017
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319513184
  • ISBN-13: 9783319513188
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319513188.html
Märksõnad:
Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations. "Computations and combinatorics in commutative algebra" has been written by experts in both theoretical and computational aspects of these three subjects and is aimed at a broad audience, from experienced researchers who want to have an easy but deep review of the topics covered to postgraduate students who need a quick introduction to the techniques. The computational treatment of the material, including plenty of examples and code, will be useful for a wide range of professionals interested in the connections between commutative algebra and combinatorics. 

1 Koszul algebras and computations, Authors: Bigatti, DeNegri.- 2 Primary decompositions, Authors: Swanson, Sáenz de Cabezón.- 3 Subdivision operations, Authors: Welker, Mohammadi.
Koszul Algebras and Computations
1(40)
Anna M. Bigatti
Emanuela De Negri
1 Introduction
1(2)
2 Presentation of Algebras
3(4)
2.1 Some Families of Subalgebras Generated by Monomials
4(3)
3 Quadratic and G-Quadratic Algebras
7(7)
3.1 Generic Initial Ideals
11(3)
4 Resolutions
14(4)
4.1 Ideals with 2-Linear Resolution
15(3)
5 Koszul Algebras and Hilbert Series
18(4)
6 G-Quadratic and LG-Quadratic Algebras
22(5)
7 Koszul Filtrations
27(4)
8 Complete Intersection of Quadrics
31(7)
9 Koszul Algebras in a Nutshell
38(3)
Primary Decompositions
41(36)
Irena Swanson
Eduardo Saenz-de-Cabezon
1 Computation of Primary Decompositions
41(11)
1.1 Introduction to Primary Ideals and Primary Decompositions
42(4)
1.2 Computing Radicals and Primary Decompositions
46(4)
1.3 Computer Experiments: Using Macaulay2 to Obtain Primary Decompositions
50(2)
2 Expanded Lectures on Binomial Ideals
52(9)
2.1 Binomial Ideals in S = k[ X1, ..., Xn, X--11,..., X=1n] = k[ X1, ..., Xn]X1 ... Xn
54(2)
2.2 Associated Primes of Binomial Ideals Are Binomial
56(1)
2.3 Primary Decomposition of Binomial Ideals
57(3)
2.4 The Radical of a Binomial Ideal Is Binomial
60(1)
3 Primary Decomposition in Algebraic Statistics
61(16)
3.1 Conditional Independence
61(3)
3.2 Intersection Axiom
64(2)
3.3 A Version of the Hammersley-Clifford Theorem
66(3)
3.4 Summary/Unification of Some Recent Papers
69(2)
3.5 A Related Game
71(1)
3.6 Binomial Edge Ideals with Macaulay2
72(1)
3.7 A Short Excursion Into Networks Using Monomial Primary Decompositions
73(4)
Combinatorics and Algebra of Geometric Subdivision Operations
77(46)
Fatemeh Mohammadi
Volkmar Welker
1 Introduction
77(2)
2 Abstract and Geometric Simplicial Complexes
79(1)
3 Subdivisions of Simplicial Complexes
80(2)
3.1 Barycentric Subdivision
81(1)
3.2 Edgewise Subdivision
81(1)
3.3 Interval Subdivision
82(1)
4 The Stanley-Reisner Ring
82(3)
5 The f- and h-Vector Transformations
85(5)
5.1 The f-Vector Transformation
85(2)
5.2 The h-Vector Transformation
87(3)
6 First Relations to Algebra
90(6)
7 Few Subdivisions, Real Rootedness, Koszul and Veronese Algebras, Charney-Davis Conjecture x
96(9)
7.1 Barycentric Subdivision
96(4)
7.2 Edgewise Subdivision
100(3)
7.3 Interval Subdivision
103(1)
7.4 Subdivisions and the Charney-Davis Conjecture
103(2)
8 Few Subdivisions, Lefschetz Properties and Real Rootedness
105(7)
8.1 Barycentric Subdivision
107(3)
8.2 Edgewise Subdivision
110(1)
8.3 Interval Subdivision
111(1)
8.4 Lefschetz Properties and Real Rootedness
111(1)
9 Many Subdivisions, Limit Behaviour
112(4)
9.1 The f- and h-Vectors
112(2)
9.2 Betti Numbers
114(2)
10 Resolutions Supported on Subdivisions
116(7)
10.1 Barycentric Subdivision
117(1)
10.2 Edgewise Subdivision
118(1)
10.3 Interval Subdivision
119(4)
References 123