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



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.



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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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA
  2. 2.Department of MathematicsUniversity of KentuckyLexingtonUSA
  3. 3.Department of Mathematical SciencesMichigan Technological UniversityHoughtonUSA

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