Abstract
The class of equidimensional polymatroidal ideals is studied. In particular, we show that an unmixed polymatroidal ideal is connected in codimension one if and only if it is Cohen-Macaulay. Especially a matroidal ideal is connected in codimension one precisely when it is a squarefree Veronese ideal. As a consequence we indicate that for polymatroidal ideals, Serre’s condition (S n ) for some n ≥ 2 is equivalent to Cohen-Macaulay property. We also give a classification of generalized Cohen-Macaulay polymatroidal ideals.
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Somayeh Bandari was in part supported by a grant from IPM (No. 92130020)
Raheleh Jafari was in part supported by a grant from IPM (No. 92130420).
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Bandari, S., Jafari, R. On certain equidimensional polymatroidal ideals. manuscripta math. 149, 223–233 (2016). https://doi.org/10.1007/s00229-015-0771-5
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DOI: https://doi.org/10.1007/s00229-015-0771-5