Inequalities for the h-Vectors and Flag h-Vectors of Geometric Lattices
نویسندگان
چکیده
منابع مشابه
Inequalities for the H- and Flag H-vectors of Geometric Lattices
We prove that the order complex of a geometric lattice has a convex ear decomposition. As a consequence, if ∆(L) is the order complex of a rank (r+1) geometric lattice L, then the for all i ≤ r/2 the h-vector of ∆(L) satisfies, hi−1 ≤ hi and hi ≤ hr−i. We also obtain several inequalities for the flag h-vector of ∆(L) by analyzing the weak Bruhat order of the symmetric group. As an application, ...
متن کاملON THE h-VECTORS OF COHEN-MACAULAY FLAG COMPLEXES
Starting from an unpublished conjecture of Kalai and from a conjecture of Eisenbud, Green and Harris, we study several problems relating h-vectors of Cohen-Macaulay, flag simplicial complexes and face vectors of simplicial complexes.
متن کاملFlag Vectors
This paper deenes for each object X that can be constructed out of a nite number of vertices and cells a vector fX lying in a nite dimensional vector space. This is the ag vector of X. It is hoped that the quantum topological invariants of a manifold M can be expressed as linear functions of the ag vector of the i-graph that arises from any suitable triangulation T of M. Flag vectors are also d...
متن کاملSUBDIVISIONS AND LOCAL h-VECTORS
In Part I a general theory of f-vectors of simplicial subdivisions (ortriangulations) of simplicial complexes is developed, based on the concept of lo-cal h-vector. As an application, we prove that the h-vector of a Cohen-Macaulaycomplex increases under "quasi-geometric" subdivision, thus establishing a spe-cial case of a conjecture of Kalai and this author. Techniques include c...
متن کاملf-vectors and h-vectors of simplicial posets
Stanely, R.P., f-vectors and h-vectors of simplicial posets, Journal of Pure and Applied Algebra 71 (1991) 319-331. A simplicial poset is a (finite) poset P with d such that every interval [6, x] is a boolean algebra. Simplicial posets are generalizations of simplicial complexes. The f-vector f(P) = (f,, f,, , ,f_,) of a simplicial poset P of rank d is defined by f; = #{x E P: [6, x] g B,, I}, ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2004
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-004-1137-z