Séminaire Lotharingien de Combinatoire, B43h (2000), 23 pp.

Jan Snellman

On some Partial Orders Associated to Generic Initial Ideals

Abstract. We study two partial orders on the free abelian monoid on a (finite or countable) set of indeterminates. These partial orders, which we call the ``strongly stable'' and the ``stable'' partial order, are defined by the property that their filters are precisely the strongly stable and the stable monoid ideals. These ideals arise in the study of generic initial ideals.

Received: April 26, 1999; Revised: October 28, 1999; Accepted: March 3, 2000.

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