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Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2020

The flag upper bound theorem for 3- and 5-manifolds

Résumé

We prove that among all flag 3-manifolds on n vertices, the join of two circles with [n 2] and [n 2] vertices respectively is the unique maximizer of the face numbers. This solves the first case of a conjecture due to Lutz and Nevo. Further, we establish a sharp upper bound on the number of edges of flag 5-manifolds and characterize the cases of equality. We also show that the inequality part of the flag upper bound conjecture continues to hold for all flag 3-dimensional Eulerian complexes and characterize the cases of equality in this class.
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Dates et versions

hal-02168183 , version 1 (28-06-2019)

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Hailun Zheng. The flag upper bound theorem for 3- and 5-manifolds. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6335⟩. ⟨hal-02168183⟩
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