The Stanley Depth in the Upper Half of the Koszul Complex |
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Authors: | Lukas Katthän |
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Institution: | Goethe-Universit?t Frankfurt, Institut für Mathematik, Frankfurt am Main, Germany |
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Abstract: | Let R = KX1, ?c, Xn] be a polynomial ring over some field K. In this article, we prove that the kth syzygy module of the residue class field K of R has Stanley depth n ? 1 for ?n/2? ≤k < n, as it had been conjectured by Bruns et al. in 2010. In particular, this gives the Stanley depth for a whole family of modules whose graded components have dimension greater than 1. So far, the Stanley depth is known only for a few examples of this type. Our proof consists in a close analysis of a matching in the Boolean algebra. |
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Keywords: | Boolean algebra Hilbert depth Koszul complex Stanley depth |
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