Related papers: Computable paradoxical decompositions

We derive the Kac-Paljutkin finite-dimensional Hopf algebras as finite fibrations of the quantum double torus and generalize the construction for quantum multiple tori.

There are significant differences between Helmholtz and Hodge's decomposition theorems, but both share a common flavor. This paper is a first step to bring them together. We here produce Helmholtz theorems for differential 1-forms and…

We investigate computability in the lattice of equivalence relations on the natural numbers. We mostly investigate whether the subsets of appropriately defined subrecursive equivalence relations -for example the set of all polynomial-time…

In this note we use the divisorial Zariski decomposition to give a more intrinsic version of the algebraic Morse inequalities.

We generalize Philip Hall's celebrated theorems on finite solvable groups to scheme theory. Our result is based on a series of results on hypergroups.

It will be shown that the polynomial time computable numbers form a field, and especially an algebraically closed field.

In this work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic…

We prove Horrocks' theorem for the odd elementary orthogonal group, which gives a decomposition of an orthogonal matrix with entries from a polynomial ring $R[X]$, over a commutative ring $R$ in which 2 is invertible, as a product of an…

An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…

One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…

We give a~detailed construction of the complete ordered field of real numbers by means of infinite decimal expansions. We prove that in the canonical encoding of decimals neither addition nor multiplication is {\em computable}, but that…

We conduct a computability-theoretic study of Ramsey-like theorems of the form "Every coloring of the edges of an infinite clique admits an infinite sub-clique avoiding some pattern", with a particular focus on transitive patterns. As it…

We discuss arithmetic and Hodge-theoretic properties of the isomorphisms appearing in the decomposition theorem for quantum cohomology of blowups. These properties underpin the application to the rationality questions by…

The paper presents a counterexample to the Hodge conjecture.

We use derived Hall algebra of the category of nilpotent representations of Jordan quiver to reconstruct the theory of symmetric functions, focusing on Hall-Littlewood symmetric functions and various operators acting on them.

An alternative characterization of Minkowski--Lyapunov functions is derived. The derived characterization enables a computationally efficient utilization of Minkowski--Lyapunov functions in arbitrary finite dimensions. Due to intrinsic…

We construct a gauged linear sigma model with two non-birational K\"alher phases which we prove to be derived equivalent, $\mathbb{L}$-equivalent, deformation equivalent and Hodge equivalent. This provides a new counterexample to the…

The paper presents results for deriving closed-form analytic solutions of the evolution of inhomogeneities in a homogeneous spatially flat multicomponent cosmological model. Mathematical methods to derive computable forms of the…

This paper examines the application of Tarski's Undefinability Theorem to first-order arithmetic. The generally accepted view is that for this case the Theorem establishes that arithmetic truth is not arithmetic. A careful examination of…

In this paper, we introduce a foundation for computable model theory of rational Pavelka logic (an extension of {\L}ukasiewicz logic) and continuous logic, and prove effective versions of some theorems in model theory. We show how to reduce…