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Paper   IPM / M / 14913
School of Mathematics
  Title:   Dimension-dependent upper bounds for Grobner bases
  Author(s):  Amir Hashemi (Joint with W. M. Seiler)
  Status:   In Proceedings
  Proceeding: Proceedings of the 2017 ACM on Inernational Symposium on symbolic and Algebraic Computation (ISSAC'17)
  Year:  2017
  Pages:   189-196
  Supported by:  IPM
We improve certain degree bounds for Grobner bases of polynomial ideals in generic position. We work exclusively in deterministically verifiable and achievable generic positions of a combinatorial nature, namely either strongly stable position or quasi stable position. Furthermore, we exhibit new dimension- (and depth-)dependent upper bounds for the Castelnuovo-Mumford regularity and the degrees of the elements of the reduced Grobner basis (w.r.t. the degree reverse lexicographical ordering) of a homogeneous ideal in these positions.

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