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ORDERINGS OF MONOMIAL IDEALS
, 2003
"... We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal invariants for the complexity of this ordered set. In particular ..."
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Cited by 4 (1 self)
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We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal invariants for the complexity of this ordered set. In particular, we give an interpretation of the height function in terms of the HilbertSamuel polynomial, and we compute upper and lower bounds on the maximal order type.
Finiteness theorems in stochastic integer programming
 Foundations of Computational Mathematics
, 2003
"... Abstract. We study Graver test sets for families of linear multistage stochastic integer programs with varying number of scenarios. We show that these test sets can be decomposed into finitely many “building blocks”, independent of the number of scenarios, and we give an effective procedure to comp ..."
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Cited by 3 (0 self)
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Abstract. We study Graver test sets for families of linear multistage stochastic integer programs with varying number of scenarios. We show that these test sets can be decomposed into finitely many “building blocks”, independent of the number of scenarios, and we give an effective procedure to compute them. The paper includes an introduction to NashWilliams ’ theory of betterquasiorderings, which is used to show termination of our algorithm. We also apply this theory to finiteness results for Hilbert functions.