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arXiv · 2405.17632

A Duality between Hilbert Functions of Lex Ideals and Quotients

Reid Buchanan
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Abstract

We study the Macaulay coefficients induced by the ideal and quotient segments of a degree-$\delta$ 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 $\{0,1,\ldots,n+\delta-2\}$.

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Reid Buchanan. 2024-05-27. A Duality between Hilbert Functions of Lex Ideals and Quotients. https://arxiv.org/abs/2405.17632

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