Abstract
To compute the local cohomology of powers of edge ideals one needs to know their saturations. The saturation of the second and third powers has been described in terms of the graph in Hien et al. (J. Algebra 439, 225–244, 2015) and Terai and Trung (J. Pure Appl. Algebra 218, 1117–1129, 2014). In this article, we give a combinatorial description of the generators of the saturation of the fourth power. As a consequence, we are able to give a complete classification of the associated primes of the fourth power of edge ideals in terms of the graph.
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Acknowledgments
The authors would like to thank Prof. Ngo Viet Trung for his guidance.
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Dedicated to Professor Ngo Viet Trung on the occasion of his sixtieth birthday
This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the grant number 101.04-2014.52. Part of the paper was written while the second author visited VIASM, Vietnam Institute for Advanced Study in Mathematics. This author would like to thank VIASM for hospitality and support.
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Thu Hien, H.T., Lam, H.M. Combinatorial Characterizations of the Saturation and the Associated Primes of the Fourth Power of Edge Ideals. Acta Math Vietnam 40, 511–526 (2015). https://doi.org/10.1007/s40306-015-0140-1
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DOI: https://doi.org/10.1007/s40306-015-0140-1