On γ-vectors satisfying the Kruskal-Katona inequalities

E. Nevo*, T. K. Petersen

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review


We present examples of flag homology spheres whose γ-vectors 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 flag simplicial complexes whose f-vectors are the γ-vectors in question, and so a result of Frohmader shows that the γ-vectors satisfy not only the Kruskal-Katona inequalities but also the stronger Frankl-Füredi-Kalai inequalities. In another direction, we show that if a flag (d - 1)-sphere has at most 2d + 3 vertices its γ-vector satisfies the Frankl-Füredi-Kalai inequalities. We conjecture that if Δ is a flag homology sphere then γ (Δ) satisfies the Kruskal-Katona, and further, the Frankl-Füredi-Kalai inequalities. This conjecture is a significant refinement of Gal's conjecture, which asserts that such γ-vectors are nonnegative.

Original languageAmerican English
Number of pages12
StatePublished - 2010
Externally publishedYes
Event22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10 - San Francisco, CA, United States
Duration: 2 Aug 20106 Aug 2010


Conference22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10
Country/TerritoryUnited States
CitySan Francisco, CA


  • Associahedron
  • Coxeter complex
  • Gal's conjecture
  • Simplicial complex
  • γ-vector


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