2024/11/26 by Archana S. Morye, Morye, Archana S, S B Sreenanda +3
Computer Science · Engineering · Mathematics · #13P10 #14Q20 #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2411.17602
openalex publication_date 2024/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we investigate the cardinality of Groebner bases under various monomial orderings. We identify a family of polynomials F and a criterion such that the reduced Groebner basis of F is double exponential in cardinality with respect to any monomial ordering which satisfies this criterion. We also show that the said criterion is satisfied by orderings such as the lexicographic, degree lexicographic and weighted orderings.