Abstract
Minimal cellular resolutions of the edge ideals of cointerval hypergraphs are constructed. This class of d-uniform hypergraphs coincides with the complements of interval graphs (for the case d = 2), and strictly contains the class of ‘strongly stable’ hypergraphs corresponding to pure shifted simplicial complexes. The polyhedral complexes supporting the resolutions are described as certain spaces of directed graph homomorphisms, and are realized as subcomplexes of mixed subdivisions of the Minkowski sums of simplices. Resolutions of more general hypergraphs are obtained by considering decompositions into cointerval hypergraphs.
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The authors would like to thank Vic Reiner for useful conversations, as well as the anonymous referee for helpful comments and corrections.
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A. Dochtermann was supported by an Alexander von Humboldt postdoctoral fellowship.
Alexander Engström is a Miller Research Fellow 2009–2012 at UC Berkeley, and gratefully acknowledges support from the Adolph C. and Mary Sprague Miller Institute for Basic Research in Science.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Dochtermann, A., Engström, A. Cellular resolutions of cointerval ideals. Math. Z. 270, 145–163 (2012). https://doi.org/10.1007/s00209-010-0789-z
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DOI: https://doi.org/10.1007/s00209-010-0789-z