A polynomial-time algorithm computes exact second-price pacing equilibria for constant numbers of goods by partitioning the multiplier space into geometric cells with fixed bid orderings and reducing each to a linear feasibility program.
Zaslavsky, Facing up to arrangements: face-count formulas for partitions of space by hyperplanes, Mem.\ Amer.\ Math.\ Soc.\ 154 (1975), vii+102 pp
4 Pith papers cite this work, alongside 637 external citations. Polarity classification is still indexing.
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Orlik–Solomon sheaf homology on a geometric lattice concentrates in top degree and decomposes as a sum of local OS algebras tensored with top homology of complementary geometric semilattices.
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Pacing Equilibria in Second-Price Auctions with Few Goods
A polynomial-time algorithm computes exact second-price pacing equilibria for constant numbers of goods by partitioning the multiplier space into geometric cells with fixed bid orderings and reducing each to a linear feasibility program.
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Orlik--Solomon sheaf homology of geometric lattices
Orlik–Solomon sheaf homology on a geometric lattice concentrates in top degree and decomposes as a sum of local OS algebras tensored with top homology of complementary geometric semilattices.
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Binary binomial equivalence via hyperplane arrangements
An explicit arrangement of n hyperplanes in 3-space indexes binary 2-binomial equivalence classes of binary words of length n, with class sizes given by coefficients of Gaussian binomials.
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AffineLens: Capturing the Continuous Piecewise Affine Functions of Neural Networks
AffineLens enumerates the maximal continuous piecewise-affine regions induced by neural networks with batch-norm, pooling, residuals and convolutions inside a bounded input polytope and supplies visualizations and region-count metrics.