Related papers: A determinacy approach to Borel combinatorics
We discuss the use of methods coming from integrable systems to study problems of enumerative and algebraic combinatorics, and develop two examples: the enumeration of Alternating Sign Matrices and related combinatorial objects, and the…
We consider several distinct characterizations of finite implication algebras. One of these leads to a new characterization of Boolean polymatroids.
We give new equivalent characterizations for ideals of Borel type. Also, we prove that the regularity of a product of ideals of Borel type is bounded by the sum of the regularities of those ideals.
We provide infinitely many solutions of a Dirichlet problem on balls.
Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem --…
We introduce a refinement of the usual Ehrenfeucht-Fra\"{\i}ss\'e game. The new game will help us make finer distinctions than the traditional one. In particular, it can be used to measure the size formulas needed for expressing a given…
This paper is about a method for solving infinite series in closed form by using inverse and forward Laplace transforms. The resulting integral is to be solved instead. The method is extended by parametrizing the series. A further Laplace…
We describe an algorithm for computing best response strategies in a class of two-player infinite games of incomplete information, defined by payoffs piecewise linear in agents' types and actions, conditional on linear comparisons of…
Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…
We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.
This is an introduction into John Conway's beautiful Combinatorial Game Theory, providing precise statements and detailed proofs for the fundamental parts of his theory. (1) Combinatorial game theory, (2) the GROUP of games, (3) the FIELD…
We initiate the study of simple games from the point of view of combinatorial topology. The starting premise is that the losing coalitions of a simple game can be identified with a simplicial complex. Various topological constructions and…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
We exhibit a class of classical or tropical posynomial systems which can be solved by reduction to linear or convex programming problems. This relies on a notion of colorful vectors with respect to a collection of Newton polytopes. This…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
We attempt to make superdeterminism more intuitive, notably by simulating a deterministic model system, a billiard game. In this system an initial 'bang' correlates all events, just as in the superdeterministic universe. We introduce the…
In this paper, we study a game with positive or plus infinite expectation and determine the optimal proportion of investment for maximizing the limit expectation of growth rate per attempt. With this objective, we introduce a new pricing…
We present a necessary and sufficient condition for a Boolean algebra to carry a finitely additive measure.
The quantum mechanical approach to the well known prisoners dilemma, one of the basic examples to illustrate the concepts of Game Theory, is implemented with a classical optical resource, nonquantum entanglement between spin and orbital…
In Problem #1542 of Mathematics Magazine, Grossman and Turett define the Cantor game. In his 2007 Mathematics Magazine article about the Cantor game, Matt Baker proves several results and poses three challenging questions about it: Do there…