000			03525cam a22005055i 4500
001			21676298
003			OSt
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006			m |o d |
007			cr |||||||||||
008			180928s2018 gw |||| o |||| 0|eng
010			_a 2019744217
020			_a9783030070199 (Pbk)
024	7		_a10.1007/978-3-319-95349-6 _2doi
035			_a(DE-He213)978-3-319-95349-6
040			_aDLC _beng _epn _erda _cIISERB
072		7	_aMAT002010 _2bisacsh
072		7	_aPBF _2bicssc
072		7	_aPBF _2thema
082	0	4	_a512.44 H44B _223
100	1		_aHerzog, Jurgen. _928098
245	1	0	_aBinomial Ideals _cby Jürgen Herzog, Takayuki Hibi, Hidefumi Ohsugi.
260			_aSwitzerland: _bSpringer Nature, _c2018.
300			_aXIX, 321 p. _c55 illustrations, 4 illustrations in color.
490	1		_aGraduate Texts in Mathematics, _x0072-5285 ; _v279
505	0		_aPart I: Basic Concepts -- Polynomial Rings and Gröbner Bases -- Review of Commutative Algebra -- Part II:Binomial Ideals and Convex Polytopes -- Introduction to Binomial Ideals -- Convex Polytopes and Unimodular Triangulations -- Part III. Applications in Combinatorics and Statistics- Edge Polytopes and Edge Rings -- Join-Meet Ideals of Finite Lattices -- Binomial Edge Ideals and Related Ideals -- Ideals Generated by 2-Minors -- Statistics -- References -- Index.
520			_aThis textbook provides an introduction to the combinatorial and statistical aspects of commutative algebra with an emphasis on binomial ideals. In addition to thorough coverage of the basic concepts and theory, it explores current trends, results, and applications of binomial ideals to other areas of mathematics. The book begins with a brief, self-contained overview of the modern theory of Gröbner bases and the necessary algebraic and homological concepts from commutative algebra. Binomials and binomial ideals are then considered in detail, along with a short introduction to convex polytopes. Chapters in the remainder of the text can be read independently and explore specific aspects of the theory of binomial ideals, including edge rings and edge polytopes, join-meet ideals of finite lattices, binomial edge ideals, ideals generated by 2-minors, and binomial ideals arising from statistics. Each chapter concludes with a set of exercises and a list of related topics and results that will complement and offer a better understanding of the material presented. Binomial Ideals is suitable for graduate students in courses on commutative algebra, algebraic combinatorics, and statistics. Additionally, researchers interested in any of these areas but familiar with only the basic facts of commutative algebra will find it to be a valuable resource.
650		0	_aCombinatorics. _928099
650		0	_aCommutative algebra. _928100
650		0	_aCommutative rings. _928101
650		0	_aConvex geometry. _928102
650		0	_aDiscrete geometry. _928103
650	1	4	_aCommutative Rings and Algebras. _928104
650	2	4	_aCombinatorics. _928099
650	2	4	_aConvex and Discrete Geometry. _928105
700	1		_aHibi, Takayuki. _928106
700	1		_aOhsugi, Hidefumi. _928107
776	0	8	_iPrint version: _tBinomial ideals _z9783319953472 _w(DLC) 2018949912
776	0	8	_iPrinted edition: _z9783030070199
776	0	8	_iPrinted edition: _z9783319953472
776	0	8	_iPrinted edition: _z9783319953489
830		0	_aGraduate Texts in Mathematics, _v279 _928108
906			_a0 _bibc _corigres _du _encip _f20 _gy-gencatlg
942			_2ddc _cBK
999			_c9744 _d9744