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Some combinatorial properties of flag simplicial pseudomanifolds and spheres

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Abstract

A simplicial complex Δ is called flag if all minimal nonfaces of Δ have at most two elements. The following are proved: First, if Δ is a flag simplicial pseudomanifold of dimension d−1, then the graph of Δ (i) is (2d−2)-vertex-connected and (ii) has a subgraph which is a subdivision of the graph of the d-dimensional cross-polytope. Second, the h-vector of a flag simplicial homology sphere Δ of dimension d−1 is minimized when Δ is the boundary complex of the d-dimensional cross-polytope.

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References

  1. Athanasiadis, C. A., On the graph connectivity of skeleta of convex polytopes, Discrete Comput. Geom.42 (2009), 155–165.

    Google Scholar 

  2. Barnette, D., Graph theorems for manifolds, Israel J. Math.16 (1973), 62–72.

    Article  MathSciNet  MATH  Google Scholar 

  3. Björner, A., Topological methods, in Handbook of Combinatorics, pp. 1819–1872, North-Holland, Amsterdam, 1995.

    Google Scholar 

  4. Gal, S. R., Real root conjecture fails for five- and higher-dimensional spheres, Discrete Comput. Geom.34 (2005), 269–284.

    Article  MathSciNet  MATH  Google Scholar 

  5. Grünbaum, B., On the facial structure of convex polytopes, Bull. Amer. Math. Soc.71 (1965), 559–560.

    Article  MathSciNet  MATH  Google Scholar 

  6. Meshulam, R., Domination numbers and homology, J. Combin. Theory Ser. A102 (2003), 321–330.

    Article  MathSciNet  MATH  Google Scholar 

  7. Nevo, E., Remarks on missing faces and generalized lower bounds on face numbers, Electron. J. Combin.16 (2009), Research Paper 8, 11 pp.

    Google Scholar 

  8. Novik, I., Personal communication, February 4, 2009.

  9. Novik, I. and Swartz, E., Face ring multiplicity via CM-connectivity sequences, Canad. J. Math.61 (2009), 888–903.

    Google Scholar 

  10. Stanley, R. P., A monotonicity property of h-vectors and h*-vectors, European J. Combin.14 (1993), 251–258.

    Article  MathSciNet  MATH  Google Scholar 

  11. Stanley, R. P., Combinatorics and Commutative Algebra, 2nd ed., Progress in Mathematics 41, Birkhäuser, Boston, 1996.

    MATH  Google Scholar 

  12. Wotzlaw, R. F., Incidence Graphs and Unneighborly Polytopes, Doctoral Dissertation, TU Berlin, 2009.

  13. Ziegler, G. M., Lectures on Polytopes, Graduate Texts in Mathematics 152, Springer, New York, 1995.

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, University of Athens, Athens, 15784, Greece

    Christos A. Athanasiadis

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  1. Christos A. Athanasiadis
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Correspondence to Christos A. Athanasiadis.

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Dedicated to Anders Björner on the occasion of his sixtieth birthday.

Supported by the 70/4/8755 ELKE Research Fund of the University of Athens.

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Athanasiadis, C.A. Some combinatorial properties of flag simplicial pseudomanifolds and spheres. Ark Mat 49, 17–29 (2011). https://doi.org/10.1007/s11512-009-0106-4

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  • DOI: https://doi.org/10.1007/s11512-009-0106-4

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