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Pure O-Sequences: Known Results, Applications, and Open Problems

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Commutative Algebra

Abstract

This paper presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also presented.

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Acknowledgements

We wish to thank David Cook II and Richard Stanley for their helpful comments. The third author also thanks Jürgen Bierbrauer for an interesting discussion on the connections between group theory and Steiner systems. We thank the referee for a careful reading of the chapter.

The work for this chapter was done while the first author was sponsored by the National Security Agency under Grant Number H98230-12-1-0204 and by the Simons Foundation under grant #208579. The work for this chapter was done while the second author was sponsored by the National Security Agency under Grant Number H98230-12-1-0247 and by the Simons Foundation under grant #208869.

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Authors and Affiliations

  1. Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Juan Migliore

  2. Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, KY, 40506-0027, USA

    Uwe Nagel

  3. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931, USA

    Fabrizio Zanello

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  1. Juan Migliore
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Correspondence to Juan Migliore .

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  1. Cornell University, 547 Malott Hall, Ithaca, 14853, New York, USA

    Irena Peeva

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Migliore, J., Nagel, U., Zanello, F. (2013). Pure O-Sequences: Known Results, Applications, and Open Problems. In: Peeva, I. (eds) Commutative Algebra. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5292-8_16

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