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arXiv · 2504.12146

Computation of dominant ideals

Anna Maria Bigatti·Nursel Erey·Selvi Kara·Augustine O'Keefe·Sonja Petrović·Pierpaola Santarsiero·Janet Striuli
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Abstract

We consider the problem of determining whether a monomial ideal is dominant. This property is critical for determining for which monomial ideals the Taylor resolution is minimal. We first analyze dominant ideals with a fixed least common multiple of generators using combinatorial methods. Then, we adopt a probabilistic approach via the \er\ type model, examining both homogeneous and non-homogeneous cases. This model offers an efficient alternative to exhaustive enumeration, allowing the study of dominance through small random samples, even in high-dimensional settings.

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Anna Maria Bigatti, Nursel Erey, Selvi Kara, Augustine O'Keefe, Sonja Petrović, Pierpaola Santarsiero, Janet Striuli. 2025-04-16. Computation of dominant ideals. https://arxiv.org/abs/2504.12146

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