Intersections of Leray complexes and regularity of monomial ideals

@article{Kalai2006IntersectionsOL,
  title={Intersections of Leray complexes and regularity of monomial ideals},
  author={G. Kalai and R. Meshulam},
  journal={J. Comb. Theory, Ser. A},
  year={2006},
  volume={113},
  pages={1586-1592}
}
  • G. Kalai, R. Meshulam
  • Published 2006
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
  • For a simplicial complex X and a field K, let h˜i(X) = dim H˜i (X; K).It is shown that if X, Y are complexes on the same vertex set, then for k ≥ 0 h˜k-1(X ∩ Y) ≤ Σσ ∈ Y Σi+j=k h˜i-1 (X[σ])ċ h˜j-1 (lk(Y, σ)).A simplicial complex X is d-Leray over K, if H˜i(Y; K) = 0 for all induced subcomplexes Y ⊂ X and i ≥ d. Let LK(X) denote the minimal d such that X is d-Leray over K. The above theorem implies that if X, Y are simplicial complexes on the same vertex set then LK(X ∩ Y) ≤ LK(X) + LK(Y… CONTINUE READING
    45 Citations

    Topics from this paper.

    Leray numbers of projections and a topological Helly-type theorem
    • 32
    • PDF
    Helly numbers of acyclic families
    The edge ideal of a graph and its splitting graphs
    Helly numbers of acyclic families
    • 12
    • PDF
    Results on the regularity of square-free monomial ideals
    • 29
    • Highly Influenced
    • PDF
    Multinerves and helly numbers of acyclic families
    • 16
    • PDF
    Dimension Gaps between Representability and Collapsibility
    • 16
    • PDF

    References

    SHOWING 1-10 OF 19 REFERENCES
    A topological colorful Helly theorem
    • 53
    Transversal numbers for hypergraphs arising in geometry
    • 82
    • PDF
    Helly, Radon, and Carathéodory Type Theorems
    • 266
    Cohen-Macaulay Rings
    • 2,361
    Topology of plane arrangements and their complements
    • 15
    Handbook of Combinatorics
    • 1,065
    On Cohen-Macaulay rings
    • 763
    • PDF
    Handbook of Convex Geometry
    • 425