MathDBKalai's conjecture for f-vectors of flag Cohen–Macaulay complexes
Kalai's conjecture for f-vectors of flag Cohen–Macaulay complexes
A simplicial complex is balanced if its graph is properly -colorable when it has dimension . Kalai's flag Cohen–Macaulay conjecture. The -vector of any flag Cohen–Macaulay complex is the -vector of a balanced Cohen–Macaulay complex. This is a stronger version of the known theorem for arbitrary flag complexes; the source does not state a resolution.
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Sources & referencesView supporting material
Primary source
Hailun Zheng, “Face enumeration on flag complexes and flag spheres”, arXiv:1809.06835 (2018).
Additional references
3 papers in this index state this conjecture (2010–2018). The statement above is taken from the most recent of them; the others are arXiv:1010.2253, arXiv:1004.0170.
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