On Γ-vectors Satisfying Kruskal-katona Inequalities
نویسنده
چکیده
We present examples of flag homology spheres whose γvectors satisfy the Kruskal-Katona inequalities. This includes several families of well-studied simplicial complexes, including Coxeter complexes and the simplicial complexes dual to the associahedron and to the cyclohedron. In another direction, we show that if a flag (d− 1)-sphere has at most 2d + 2 vertices its γ-vector satisfies the Kruskal-Katona inequalities. We conjecture that if ∆ is a flag homology sphere then γ(∆) satisfies the Kruskal-Katona inequalities. This conjecture is a significant refinement of Gal’s conjecture, which asserts that such γ-vectors are nonnegative.
منابع مشابه
On γ-Vectors Satisfying the Kruskal-Katona Inequalities
We present examples of flag homology spheres whose γvectors satisfy the Kruskal-Katona inequalities. This includes several families of well-studied simplicial complexes, including Coxeter complexes and the simplicial complexes dual to the associahedron and to the cyclohedron. In these cases, we construct explicit simplicial complexes whose f -vectors are the γ-vectors in question. In another di...
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