Computation of Macaulay Constants and Degree Bounds for Gröbner Bases

Co-author(s): Amir Hashemi and Hossein Parnian

Reference: Journal of Symbolic Computation, 111 (2022) 44-60

Description: This paper continues and extends our previous works [40, 46] . Following an approach developed by Dube and by applying the Hilbert series method, we provide an efficient algorithm to compute the Macaulay constants of a monomial ideal without computing any exact cone decomposition of the corresponding quotient ring. Combining it with a method proposed by Mayr and Ritscher, we derive a new upper bound for the maximum degree of the elements of any reduced Gröbner basis of an ideal generated by a set of homogeneous polynomials which depends on Krull dimension and the maximal degree of a generator of the considered ideal.

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