A Partition Theorem for Euclidean n-Space

DOI10.2307/2033091zbMath0117.37901OpenAlexW4231725351MaRDI QIDQ5728041

Oscar Wesler, Robert M. Thrall, Hans Samelson

Publication date: 1958

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2033091

zbMATH Keywords

analytic geometry, projective geometry

Related Items

Iterative methods for variational and complementarity problems, Modified Lagrange multiplier tests for problems with one-sided alternatives, The linear complementarity problem and a subclass of fully semimonotone matrices, Global uniqueness and solvability for tensor complementarity problems, Global uniqueness and solvability of tensor variational inequalities, On a subclass of \(P_ 0\), Reducing horizontal linear complementarity problems, The complementarity problem, Extended \(P\)-pairs, Stationary states of the Hartline-Ratliff model, Pivoting in linear complementarity: Two polynomial-time cases, A quadratically convergent \(\text{O}((\kappa +1)\sqrt n L)\)-iteration algorithm for the \(P_ *(\kappa)\)-matrix linear complementarity problem, Structure properties of W matrices, Linear complementarity problems with an invariant number of solutions, Theorems of Perron-Frobenius type for matrices without sign restrictions, A criterion for the convergence of the Mellin-Barnes integral for solutions to simultaneous algebraic equations, Sign reversing and matrix classes, Sufficient matrices and the linear complementarity problem, On branching numbers of normal manifolds, A lower bound on the iterative complexity of the Harker and Pang globalization technique of the Newton-min algorithm for solving the linear complementarity problem, Equations on monotone graphs, An \((m+1)\)-step iterative method of convergence order \((m+2)\) for linear complementarity problems. An \((m+1)\)-step iterative method for LCPs, Variational problem in the non-negative orthant of \(\mathbb{R}^{3}\): reflective faces and boundary influence cones, Combinatorial characterizations of \(K\)-matrices, On variational inequalities over polyhedral sets, Complementarity in Oriented Matroids, Q-matrices and spherical geometry, Exact computation of an error bound for the balanced linear complementarity problem with unique solution, More on matrix splitting modulus-based iterative methods for solving linear complementarity problem, Observations on a class of nasty linear complementarity problems, Total negativity: characterizations and single-vector tests, A polynomial-time algorithm for the tridiagonal and Hessenberg P-matrix linear complementarity problem, The nonsmooth Newton's method for the horizontal nonlinear complementarity problem, Characterizing total positivity: Single vector tests via linear complementarity, sign non‐reversal and variation diminution, Polyhedral sets having a least element, Using vector divisions in solving the linear complementarity problem, Monotone solutions of the parametric linear complementarity problem, Matrices and the linear complementarity problem, On the parametric linear complementarity problem: A generalized solution procedure, A finite characterization ofK-matrices in dimensions less than four, Counting unique-sink orientations, On spherically convex sets and \(Q\)-matrices, Relationships of properties of piecewise affine maps over ordered fields, Recent development in computational complexity characterization of Nash equilibrium, Iterative algorithms for the linear complementarity problem, On characterizing \(N\)-matrices using linear complementarity, Enumeration of PLCP-orientations of the 4-cube, A note on a characterization of \(P\)-matrices, Newton's method for linear complementarity problems, A new resolution method for the parametric linear complementarity problem, Networks of common property resources, Equilibrium existence and uniqueness in network games with additive preferences, A new proof of Robinson's homeomorphism theorem for pl-normal maps, Unnamed Item, Some P-properties for linear transformations on Euclidean Jordan algebras, On a characterization of P-matrices, On the existence and uniqueness of solutions in nonlinear complementarity theory, On the number of solutions to a class of linear complementarity problems, Isotone solutions of parametric linear complementarity problems, On monotonicity in parametric linear complementarity problems, New characterizations of the matrix classes \(\mathbf{P}\), \(\mathbf{W}\) and \(\mathbf{R}_0\), Nonconvergence of the plain Newton-min algorithm for linear complementarity problems with a \(P\)-matrix, Tensor complementarity problems. I: Basic theory, Piecewise affine bijections of \(\mathbb R^n\), and the equation \(Sx^ +- Tx^ -=y\), Sur la récurrence positivedu mouvement brownien réflechidans l'orthant positif de, Total dual integrality and integral solutions of the linear complementarity problem, On the solution of large, structured linear complementarity problems: The tridiagonal case, A reduction theorem for the linear complementarity problem with a certain patterned matrix, On a class of least-element complementarity problems, On univalence and P-matrices, Hidden Z-matrices with positive principal minors, Systems of linear interval equations, Variational inequalities and the pricing of American options, Nonstationary extrapolated modulus algorithms for the solution of the linear complementarity problem, Existence theory for generalized nonlinear complementarity problems, Uniqueness and differentiability of solutions of parametric nonlinear complementarity problems, On the number of solutions to a class of complementarity problems, A finite improvement algorithm for the linear complementarity problem, An Algorithmic Characterization of P-matricity II: Adjustments, Refinements, and Validation, On the number of solutions to the complementarity problem and spanning properties of complementary cones, A unification of two classes ofQ-matrices, On column competent matrices and linear complementarity problem, A sign-based linear method for horizontal linear complementarity problems, On the uniqueness of solutions to linear complementarity problems, Some properties of \(Q\)-matrices, On local \(w\)-uniqueness of solutions to linear complementarity problem, Degeneracy in linear complementarity problems: A survey, Ky Fan's \(N\)-matrices and linear complementarity problems, On total functions, existence theorems and computational complexity, Nonsingularity and $P$-matrices., On the connectedness of the solution set to linear complementarity systems, On \(P\)-matrices