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Monomial ideals with tiny squares (1801.07672v1)
Published 23 Jan 2018 in math.AC and math.CO
Abstract: Let $I \subset K[x,y]$ be a monomial ideal. How small can $\mu(I2)$ be in terms of $\mu(I)$? It has been expected that the inequality $\mu(I2) > \mu(I)$ should hold whenever $\mu(I) \ge 2$. Here we disprove this expectation and provide a somewhat surprising answer to the above question.
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