@article{MAYR201378,
    Abstract = {Given a basis F of a polynomial ideal I in K[x1,{\ldots},xn] with degrees deg(F)≤d, the degrees of the reduced Gr{\"o}bner basis G w.r.t. any admissible monomial ordering are known to be double exponential in the number of indeterminates in the worst case, i.e. deg(G)=d2Θ(n). This was established in Mayr and Meyer (1982) andDub{\'e} (1990). We modify both constructions in order to give worst case bounds depending on the ideal dimension proving that deg(G)=dnΘ(1)2Θ(r) for r-dimensional ideals (in the worst case).},
    Author = {Mayr, Ernst W. and Ritscher, Stephan},
    File = {Dimension-dependent bounds for Gröbner bases of polynomial ideals.pdf},
    ISSN = {0747-7171},
    Journal = {Journal of Symbolic Computation},
    Keywords = {Gr{\"o}bner basis, Degree bound, Polynomial ideal, Ideal dimension, Regular sequence, Noether normalization, Cone decomposition},
    Note = {The International Symposium on Symbolic and Algebraic Computation},
    Pages = {78-94},
    Title = {Dimension-dependent bounds for Gr{\"o}bner bases of polynomial ideals},
    URL = {https://www.sciencedirect.com/science/article/pii/S0747717111002112},
    Volume = {49},
    Year = {2013},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0747717111002112},
    bdsk-url-2 = {https://doi.org/10.1016/j.jsc.2011.12.018},
    date-added = {2021-11-19 11:56:02 +0100},
    date-modified = {2021-11-19 11:56:02 +0100},
    doi = {10.1016/j.jsc.2011.12.018}
}

@article{MAYR201378, Abstract = {Given a basis F of a polynomial ideal I in K[x1,{\ldots},xn] with degrees deg(F)≤d, the degrees of the reduced Gr{\"o}bner basis G w.r.t. any admissible monomial ordering are known to be double exponential in the number of indeterminates in the worst case, i.e. deg(G)=d2Θ(n). This was established in Mayr and Meyer (1982) andDub{\'e} (1990). We modify both constructions in order to give worst case bounds depending on the ideal dimension proving that deg(G)=dnΘ(1)2Θ(r) for r-dimensional ideals (in the worst case).}, Author = {Mayr, Ernst W. and Ritscher, Stephan}, File = {Dimension-dependent bounds for Gröbner bases of polynomial ideals.pdf}, ISSN = {0747-7171}, Journal = {Journal of Symbolic Computation}, Keywords = {Gr{\"o}bner basis, Degree bound, Polynomial ideal, Ideal dimension, Regular sequence, Noether normalization, Cone decomposition}, Note = {The International Symposium on Symbolic and Algebraic Computation}, Pages = {78-94}, Title = {Dimension-dependent bounds for Gr{\"o}bner bases of polynomial ideals}, URL = {https://www.sciencedirect.com/science/article/pii/S0747717111002112}, Volume = {49}, Year = {2013}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0747717111002112}, bdsk-url-2 = {https://doi.org/10.1016/j.jsc.2011.12.018}, date-added = {2021-11-19 11:56:02 +0100}, date-modified = {2021-11-19 11:56:02 +0100}, doi = {10.1016/j.jsc.2011.12.018} }