000			02133 a2200277 4500
999			_c51844 _d51844
008			191213b ||||| |||| 00| 0 eng d
020			_a9780817643690
082			_a512​.24 STA
100			_aStanley, Richard
245			_aCombinatorics and commutative algebra
250			_a2nd ed.
260			_bBirkhäuser, _c1996 _aBoston:
300			_a164p. _bpb; _c20 cm
365			_aEURO _b59.99
440			_aProgress in mathematics; Vol.41
520			_aSome remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for non-specialists. New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to f-vectors. Included in this chapter is an outline of the proof of McMullen's g-conjecture for simplicial polytopes based on toric varieties, as well as a discussion of the face rings of such special classes of simplicial complexes as shellable complexes, matroid complexes, level complexes, doubly Cohen-Macaulay complexes, balanced complexes, order complexes, flag complexes, relative complexes, and complexes with group actions. Also included is information on subcomplexes and subdivisions of simplicial complexes, and an application to spline theory.
650			_aGeometry, Algebraic
650			_aCommutative algebra
650			_aCommutative rings
650			_aCombinatorics
650			_aMathematics
650			_aCommutative Rings and Algebras
650			_aTopology
650			_aCombinatorial analysis
942			_2ddc _cTD