This analysis reveals formulas for extremal Betti numbers in weighted hyperplanes, highlighting pseudo-Gorenstein ideals.
In this paper, we shall provide explicit formulas for the extremal Betti numbers of $R/I$, where I is the defining ideal of certain weighted hyperplanes in Pⁿ⁻¹ and R is the polynomial ring in n indeterminates over a field. As a consequence, we completely classify such ideals which are pseudo-Gorenstein as in sense of V. Ene, J. Herzog, T. Hibi and S. S. Madani.
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Lôc et al. (2025) studied this question.
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