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Journal of Mathematical Sciences

, Volume 182, Issue 2, pp 144–158 | Cite as

Faces of faces of the acyclic Birkhoff polytope

  • L. CostaEmail author
  • E. A. Martins
Article

Abstract

Given a p-face of the acyclic Birkhoff polytope Ω n (T), where T is a tree with n vertices, we find the number of faces of lower dimension that are contained in it, and its nature is discussed.

Keywords

Open Vertex Lower Dimension Edge Incident Convex Polyhedron Common Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    G. Birkhoff, “Tres observaciones sobre el algebra lineal,” Univ. Nac. de Tucumán Rev. Sér. A, 5, 147–151 (1946).MathSciNetzbMATHGoogle Scholar
  2. 2.
    R. Brualdi, “Convex polytopes of permutation invariant doubly stochastic matrices,” J. Combin. Theory, 23, 58–67 (1977).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    R. Brualdi and P. Gibson, “Convex polyhedra of doubly stochastic matrices, II. Graph of Ωn,” J. Combin. Theory, 22, 175–198 (1977).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    R. Brualdi and P. Gibson, “Convex polyhedra of doubly stochastic matrices, III. Affine and combinatorial properties of Ωn,” J. Combin. Theory, 22, 338–351 (1977).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    L. Costa, C. M. da Fonseca, and E. A. Martins, “The diameter of the acyclic Birkhoff polytope,” Linear Algebra Appl., 428, 1524–1537 (2008).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    L. Costa, C. M. da Fonseca, and E. A. Martins, “Face counting on acyclic Birkhoff polytope,” Linear Algebra Appl., 430, 1216–1235 (2009).MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    L. Costa and E. A. Martins, “Faces of faces of the tridiagonal Birkhoff polytope,” Linear Algebra Appl., 432, No. 6, 1384–1404 (2010).MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    G. Dahl, “Tridiagonal doubly stochastic matrices,” Linear Algebra Appl., 390, 197–208 (2004).MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    C. M. da Fonseca and E. Marques de Sá, “Fibonacci numbers, alternating parity sequences and faces of the tridiagonal Birkhoff polytope,” Discr. Math., 308, No. 7, 1308–1318 (2008).zbMATHCrossRefGoogle Scholar
  10. 10.
    C. Godsil and G. Royle, Algebraic Graph Theory, Springer-Verlag, New York (2001).zbMATHCrossRefGoogle Scholar
  11. 11.
    B. Grünbaum, Convex Polytopes, Springer-Verlag, New York (2003).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AveiroAveiroPortugal

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