# Powers of Principal Q-Borel ideals Academic Article

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### abstract

• AbstractFix 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.

### publication date

• September 2022