Distinct monomial orders with same induced orderings

2014/09/24 by Gabriel Sosa, Sosa, Gabriel
Mathematics · #06A05 #13P05 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1409.7004

openalex publication_date 2014/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the lexicographic, degree lexicographic and the degree reverse lexicographic orders for monomials in R_n=K[X₁,...X_n] are uniquely determined by their induced orderings, (i.e. their restrictions to R_n,i=K[X₁,..., X_i, .., X_n]), when n ≥ 4. We also show that for any n ≥ 4 there are monomial orders that are not uniquely determined by their induced orderings, and provide examples of these orders for each n.

Related

• The converse of a theorem by Bayer and Stillman
• Valuative dimension and monomial orders
• Euclidean algorithm for a class of linear orders
• Toward a Theory of Monomial Preorders
• Linear orderings of combinatorial cubes