Mircea Cimpoeas: A generalization of Pardue's formula, p.315-334

Abstract:

In this paper, we introduce a new class of monomial ideals, called $\de$-fixed ideals, which generalize the class of $p$-Borel ideals and show how some results for $p$-Borel ideals can be transfered to this new class. In particular, we give the form of a principal $\de$-fixed ideal and we compute the socle of factors of this ideals. This allowed us to give a generalization of Pardue's formula, i.e. a formula of the regularity for a principal $\de$-fixed ideal.

Key Words: p-Borel ideals, Betti numbers, Mumford-Castelnuovo regularity.

2000 Mathematics Subject Classification: Primary: 13P10,
Secondary: 13D25, 13D02, 13H10.

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