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Random Gale diagrams and neighborly polytopes in high dimensions
Taking up a suggestion of David Gale from 1956, we generate sets of combinatorially isomorphic polytopes by choosing their Gale diagrams at random....
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Poisson equation and discrete one-sided Hilbert transform for (C, α)-bounded operators
We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for ( C , α )-bounded operators, α >...
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Combining Realization Space Models of Polytopes
In this paper we examine four different models for the realization space of a polytope: the classical model, the Grassmannian model, the Gale...
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Maximum Rectilinear Crossing Number of Uniform Hypergraphs
We improve the lower bound on the d -dimensional rectilinear crossing number of the complete d -uniform hypergraph having 2 d vertices to
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Rectilinear Crossings in Complete Balanced d-Partite d-Uniform Hypergraphs
In this paper, we study the embedding of a complete balanced d -partite d -uniform hypergraph with its nd vertices represented as points in general...
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Conditional inference of Poisson models and information geometry: an ancillary review
The Poisson distribution is a fundamental tool in categorical data analysis. This paper reviews conditional inference for the independent Poisson...
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Optimality Conditions Based on Theorems of the Alternative
In this chapter we prove again Fritz John (FJ) conditions (and then KKT conditions, under constraint qualifications) following the geometric approach...
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Urban Big Data: City Management and Real Estate Markets
In this chapter we discuss recent trends in the application of urban big data and their impact on real estate markets. We expect such technologies to...
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Manifolds of Triangulations, Braid Groups of Manifolds, and the Groups \(\Gamma _{n}^{k}\)
The spaces of triangulations of a given manifold have been widely studied. The celebrated theorem of Pachner (Eur J Comb 12:129–145, 1991) says that...
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Appendix B Origins
Euler’s differential equations represent the motion of a free rigid body in three space. Invariants of this motion are given by the kinetic energy...
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Historical steps of development of convexity as a field
In this chapter we will show historical steps of the development of convexity as a field and, in addition, developments of the relations between...
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Cremona Orbits in \(\mathbb {P}^4\) and Applications
This article is motivated by the authors’ interest in the geometry of the Mori dream space...
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Flag Matroids: Algebra and Geometry
Matroids are ubiquitous in modern combinatorics. As discovered by Gel’fand, Goresky, MacPherson and Serganova there is a beautiful connection between...
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Quasi-random multilinear polynomials
We consider multilinear Littlewood polynomials, polynomials in n variables in which a specified set of monomials U have ±1 coefficients, and all...
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Effective methods for plane quartics, their theta characteristics and the Scorza map
This is a revised version of the lecture notes prepared for the workshop on “Plane quartics, Scorza map and related topics”, held in Catania, January...
