A Duality between Hilbert Functions of Lex Ideals and Quotients
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917677116686336 |
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| author | Buchanan, Reid |
| author_facet | Buchanan, Reid |
| contents | We study the Macaulay coefficients induced by the ideal and quotient segments of a degree-$δ$ monomial in $n$ variables. We give explicit formulas for these coefficients and establish a duality between the two theories. Our main result is that the ideal and quotient coefficients form a set partition of $\{0,1,\ldots,n+δ-2\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17632 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Duality between Hilbert Functions of Lex Ideals and Quotients Buchanan, Reid Commutative Algebra 13F55, 05E40, 13D40, 13F20 We study the Macaulay coefficients induced by the ideal and quotient segments of a degree-$δ$ monomial in $n$ variables. We give explicit formulas for these coefficients and establish a duality between the two theories. Our main result is that the ideal and quotient coefficients form a set partition of $\{0,1,\ldots,n+δ-2\}$. |
| title | A Duality between Hilbert Functions of Lex Ideals and Quotients |
| topic | Commutative Algebra 13F55, 05E40, 13D40, 13F20 |
| url | https://arxiv.org/abs/2405.17632 |