Borel-plus-powers monomial ideals

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Abstract

Let S = K [x1, ..., xn] be a standard graded polynomial ring over a field K. In this paper, we show that the lex-plus-powers ideal has the largest graded Betti numbers among all Borel-plus-powers monomial ideals with the same Hilbert function. In addition in the case of characteristic 0, by using this result, we prove the lex-plus-powers conjecture for graded ideals containing x1p, ..., xnp, where p is a prime number.

Original languageEnglish
Pages (from-to)1321-1336
Number of pages16
JournalJournal of Pure and Applied Algebra
Volume212
Issue number6
DOIs
Publication statusPublished - 2008 Jun 1

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ASJC Scopus subject areas

  • Algebra and Number Theory

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