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Powers of Principal Q-Borel ideals

Part of: Algebraic combinatorics

Published online by Cambridge University Press:  23 August 2021

Eduardo Camps-Moreno ,
Craig Kohne ,
Eliseo Sarmiento  and
Adam Van Tuyl
Eduardo Camps-Moreno*
Affiliation:
Escuela Superior de Física y Matemáticas, Mexico City, Mexico
Craig Kohne
Affiliation:
McMaster University, Hamilton, ON, Canada e-mail: [email protected]
Eliseo Sarmiento
Affiliation:
Escuela Superior de Física y Matemáticas, Mexico City, Mexico e-mail: [email protected]
Adam Van Tuyl
Affiliation:
McMaster University, Hamilton, ON, Canada e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

Fix a poset Q on $\{x_1,\ldots ,x_n\}$ . A Q-Borel monomial ideal $I \subseteq \mathbb {K}[x_1,\ldots ,x_n]$ is a monomial ideal whose monomials are closed under the Borel-like moves induced by Q. A monomial ideal I is a principal Q-Borel ideal, denoted $I=Q(m)$ , if there is a monomial m such that all the minimal generators of I can be obtained via Q-Borel moves from m. In this paper we study powers of principal Q-Borel ideals. Among our results, we show that all powers of $Q(m)$ agree with their symbolic powers, and that the ideal $Q(m)$ satisfies the persistence property for associated primes. We also compute the analytic spread of $Q(m)$ in terms of the poset Q.

Keywords

monomial idealsQ-Borelsymbolic powersanalytic spreadpersistence of primes

MSC classification

Primary: 05E40: Combinatorial aspects of commutative algebra
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 3 , September 2022 , pp. 633 - 652
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

Camps is supported by Conacyt. Sarmiento’s research is supported by SNI-Conacyt. Camps and Sarmiento are supported by PIFI IPN 20201016. Van Tuyl’s research is supported by NSERC Discovery Grant 2019-05412.

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