The number of small semispaces of a finite set of points in the plane
Journal of Combinatorial Theory Series A
Voronoi diagrams and arrangements
Discrete & Computational Geometry
Halfspace range search: an algorithmic application of k-sets
Discrete & Computational Geometry
More on k-sets of finite sets in the plane
Discrete & Computational Geometry
On k-hulls and related problems
SIAM Journal on Computing
On the number of halving planes
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Output sensitive construction of levels and Voronoi diagrams in Rd of order 1 to k
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
On levels in arrangements and Voronoi diagrams
Discrete & Computational Geometry
Points and triangles in the plane and halving planes in space
Discrete & Computational Geometry
An upper bound on the number of planar K-sets
Discrete & Computational Geometry
On geometric optimization with few violated constraints
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
On the bichromatic k-set problem
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On the bichromatic k-set problem
ACM Transactions on Algorithms (TALG)
Absolute approximation of Tukey depth: Theory and experiments
Computational Geometry: Theory and Applications
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In this note, we generalize theh-vector for simple, bounded convexpolytopes [14] to the h-matrix forsimple, bounded k-complexes. Weobserve that the h-matrix isinvariant with respect to the defining linear function, and that theDehn-Sommerville relations and McMullen's Upper Bound Theorem [13] forconvex polytopes follow from the invariance ofthe 0-th row and column ofthis matrix. The invariance of the other entries in theh-matrix should, perhaps, beinvestigated more. One new consequence is that, given any non-degeneratelinear function z, the number oflocal z-minima on thelth level of anyd-dimensional arrangement is boundedby l+d-1d-1, with exact equality if thel-th level is bounded andsimple.