## Computational Commutative Algebra and CombinatoricsThis volume constitutes the proceedings of the International Conference on ``Computational Commutative Algebra and Combinatorics'' held in Osaka, Japan. It contains excellent survey articles and research papers on various topics related to the theme of the conference. Of particular interest are two survey articles, ``Algebraic Shifting'' by Gil Kalai and ``Generic Initial Ideals and Graded Betti Numbers'' by Jurgen Herzog. The volume is suitable for graduate students and research mathematicians interested in discrete mathematics. |

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### Contents

Winfried BRUNS and Joseph GUBELADZE Polyhedral Algebras | 1 |

DUVAL Algebraic Shifting and Spectral Sequences | 53 |

Jürgen HERZOG Generic Initial Ideals and Graded Betti Num | 75 |

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action affine algebraic shifting algebraic topology ample apply arrangement assume automorphism Betti numbers bound called closed Cohen-Macaulay cohomology column combinatorial commutative algebra component Conjecture connected consider contains Corollary corresponding defined definition denote determined dimension discuss element embedding equality equivalent exact example exists exterior face facet fact fiber field finite fixed follows function geometry give given graded graph Hence Hilbert homogeneous homology ideal implies inclusion induced intersection irreducible isomorphism lattice lattice polyhedral complex Lemma linear Math matrix maximal minimal module monomial monomial ideal natural normal Note obtained particular polynomial polytopes Problem projective proof properties Proposition prove quotient relation Remark respect result ring satisfies sequence simplicial complex singular space squarefree strongly stable structure subset Suppose symmetric Theorem theory toric trivial unique varieties vector vertices