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Contents.- Preface to the Second Edition.- Preface to the First Edition.- Notation.- Background: Combinatorics.- Commutative algebra and homological algebra.- Topology.- Chapter I: Nonnegative Integral Solutions to Linear Equations: Integer shastic matrices (magic squares).- Graded algebras and modules.- Elementary aspects of N-solutions to linear equations.- Integer shastic matrices again.- Dimension, depth, and Cohen-Macaulay modules.- Local cohomology.- Local cohomology of the modules M phi,alpha.- Reciprocity.- Reciprocity for integer shastic matrices.- Rational points in integer polytopes.- Free resolutions.- Duality and canonical modules.- A final look at linear equations.- Chapter II: The Face Ring of a Simplicial Complex: Elementary properties of the face ring.- f-vectors and h-vectors of complexes and multicomplexes.- Cohen-Macaulay complexes and the Upper Bound Conjecture.- Homological properties of face rings.- Gorenstein face rings.- Gorenstein Hilbert Functions.- Canonical modules of face rings.- Buchsbaum complexes.- Chapter III: Further Aspects of Face Rings: Simplicial polytopes, toric varieties, and the g-theorem.- Shellable simplicial complexes.- Matroid complexes, level complexes, and doubly Cohen-Macaulay complexes.- Balances complexes, order complexes, and flag complexes.- Splines.- Algebras with straightening law and simplical posets.- Relative simplical complexes.- Group actions.- Subcomplexes.- Subdivisions.- Problems on Simplicial Complexes and their Face Rings.- Bibliography.- Index.
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Sess Sola
reviewed Combinatorics and commutative algebra on December 14, 2011
Combinatorics and commutative algebra
Schlereth provides a lengthy, but useful and insightful introduction tracing various approaches to American material cultural studies, and defining it as a mode of inquiry with a historical basis. He focuses on historical, rather than art historical material culture, which tends toward the aesthetic rather than the analytic. He divides material culture studies into three chronological phases: Collecting/Classifying, Descriptive/Historical, and Analytical/Explanatory. Following Schlereth's introduction, is an anthology of material cultural essays devoted to theory, method, and implemented practice, concluding with a short bibliographic essay. An exemplary and engaging collection.
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Add Combinatorics and commutative algebra, * Stanley represents a broad perspective with respect to two significant topics from Combinatorial Commutative Algebra: 1) The theory of invariants of a torus acting linearly on a polynomial ring, and 2) The face ring of a simplicial complex * In, Combinatorics and commutative algebra to the inventory that you are selling on WonderClubX
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Add Combinatorics and commutative algebra, * Stanley represents a broad perspective with respect to two significant topics from Combinatorial Commutative Algebra: 1) The theory of invariants of a torus acting linearly on a polynomial ring, and 2) The face ring of a simplicial complex * In, Combinatorics and commutative algebra to your collection on WonderClub |
