Maximum linearizations of lower sets in ℕ^m with application to monomial ideals

2019/09/15 by Harry Altman, Altman, Harry, Andreas Weiermann +1
Computer Science · Mathematics · #03E10 #Commutative Algebra and Its Applications #FOS: Mathematics #Logic (math.LO) #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1909.06719

openalex publication_date 2019/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the type (maximum linearization) of the well partial order of bounded lower sets in ℕ^m, ordered under inclusion, and find it is ω^ω^m-1. Moreover we compute the type of the set of all lower sets in ℕ^m, a topic studied by Aschenbrenner and Pong, and find that it is equal to ω^∑_k=1^m ω^m-k\binommk-1 + 1. As a consequence we deduce corresponding bounds on effectively given sequences of monomial ideals in F[X,Y] where F is a field.

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