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Regularity of Squarefree Monomial Ideals

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Connections Between Algebra, Combinatorics, and Geometry

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 76))

Abstract

We survey a number of recent studies of the Castelnuovo–Mumford regularity of squarefree monomial ideals. Our focus is on bounds and exact values for the regularity in terms of combinatorial data from associated simplicial complexes and/or hypergraphs.

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Acknowledgments

The author would like to thank an anonymous referee for a careful reading and many helpful comments. The author would also like to thank S.A. Seyed Fakhari for pointing out a mistake in our original definition of H E in Theorem 3.5.

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Authors and Affiliations

  1. Department of Mathematics, Tulane University, 6823 St. Charles Ave., New Orleans, LA, 70118, USA

    Huy Tài Hà

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  1. Huy Tài Hà
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Correspondence to Huy Tài Hà .

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Editors and Affiliations

  1. Department of Mathematics, Central Michigan University, Mt. Pleasant, Michigan, USA

    Susan M. Cooper

  2. Department of Mathematics, North Dakota State University, Fargo, North Dakota, USA

    Sean Sather-Wagstaff

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Dedicated to Tony Geramita, a great teacher, colleague and friend.

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Hà, H.T. (2014). Regularity of Squarefree Monomial Ideals. In: Cooper, S., Sather-Wagstaff, S. (eds) Connections Between Algebra, Combinatorics, and Geometry. Springer Proceedings in Mathematics & Statistics, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0626-0_7

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