Computation of dominant ideals
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arXiv
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| Hauptverfasser: | , , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913796532994048 |
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| author | Bigatti, Anna Maria Erey, Nursel Kara, Selvi O'Keefe, Augustine Petrović, Sonja Santarsiero, Pierpaola Striuli, Janet |
| author_facet | Bigatti, Anna Maria Erey, Nursel Kara, Selvi O'Keefe, Augustine Petrović, Sonja Santarsiero, Pierpaola Striuli, Janet |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12146 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computation of dominant ideals Bigatti, Anna Maria Erey, Nursel Kara, Selvi O'Keefe, Augustine Petrović, Sonja Santarsiero, Pierpaola Striuli, Janet Commutative Algebra Combinatorics 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. |
| title | Computation of dominant ideals |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2504.12146 |