Order

, Volume 32, Issue 2, pp 293–299 | Cite as

Standard Examples as Subposets of Posets

Article

Abstract

We prove that a poset with no induced subposet Sk (for fixed k≥3) must have dimension that is sublinear in terms of the number of elements.

Keywords

Poset Dimension Standard example Stability 

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References

  1. 1.
    Problems in combinatorics and posets workshop, Jagiellonian University, Kraków, Poland (2012)Google Scholar
  2. 2.
    Biró, C., Füredi, Z., Jahanbekam, S.: Large chromatic number and Ramsey graphs. Graphs Combin. 29 (5), 1183–1191 (2013)MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Csaba Biró: Peter Hamburger, and Attila Pór, Large standard examples in posets with high dimension and fractional dimension, Submitted (2014)Google Scholar
  4. 4.
    Bogart, K.P., Trotter, W.T.: Maximal dimensional partially ordered sets. II. Characterization of 2n-element posets with dimension n. Discrete Math. 5, 33–43 (1973)MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Dushnik, B., Miller, E.W.: Partially ordered sets. Amer. J. Math. 63, 600–610 (1941)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hiraguchi, T.: On the dimension of orders. Sci. Rep. Kanazawa Univ. 4 (1), 1–20 (1955)MathSciNetGoogle Scholar
  7. 7.
    Kimble, R.J.: Extremal problems in dimension theory for partially ordered sets. Ph.D. thesis, Massachusetts Institute of Technology (1973)Google Scholar
  8. 8.
    William, T.: Trotter, Combinatorics and Partially Ordered Sets. The Johns Hopkins University Press (1992)Google Scholar
  9. 9.
    Partially ordered sets. In: Graham, R.L., Grötschel, M., Lovász, L. (eds.) Handbook of Combinatorics, vol. 1, pp. 433–480. Elsevier Science B. V. (1995)Google Scholar
  10. 10.
    Douglas, B.: West, Introduction to Graph Theory. Prentice Hall, Inc., Upper Saddle River (1996)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of LouisvilleLouisvilleUSA
  2. 2.Department of MathematicsWestern Kentucky UniversityBowling GreenUSA

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