Related papers: Computable paradoxical decompositions
We prove a computable version of the Hall Harem Theorem where the matching realizes a unary function with controlled sizes of cycles. We apply it to non-amenable computable coarse spaces. As a result, we obtain a computable version of the…
We prove a new version of Hall's Harem Theorem, where the final matching is realized by a unary function with additional conditions on behavior of cycles. The present paper can be considered as a helpful companion of the paper of the…
We generalize the logarithmic decomposition theorem of Deligne-Illusie to a filtered version. There are two applications. The easier one provides a mod $p$ proof for a vanishing theorem in characteristic zero. The deeper one gives rise to a…
We descibed all alternative algebras with invertible derivations (the analogue of Bergen-Herstein-Lanski's Theorem) and proved the analogue of Moens's Theorem.
We introduce a notion of algorithmic randomness for algebraic fields. We prove the existence of a continuum of algebraic extensions of $\mathbb{Q}$ that are random according to our definition. We show that there are noncomputable algebraic…
Certain computable polynomials are described whose leading coefficients are equal to multiplicities in the tensor product decomposition for representations of a Lie algebra of ADE type.
Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…
We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of…
The notion of computable reducibility between equivalence relations on the natural numbers provides a natural computable analogue of Borel reducibility. We investigate the computable reducibility hierarchy, comparing and contrasting it with…
In this paper, we establish the theory of $\sigma$-solvable hypergroups, study some properties of $\sigma$-solvable hypergroups and give similar results of Hall's Theorem in $\sigma$-solvable hypergroups.
We establish primitive recursive versions of some known facts about computable ordered fields of reals and computable reals, and then apply them to proving primitive recursiveness of some natural problems in linear algebra and analysis. In…
In this paper, we give a bijective proof of the reduced lecture hall partition theorem. It is possible to extend this bijection in lecture hall partition theorem. And refined versions of each theorems are also presented.
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
We present an alternative proof of the Alexander-Hirschowitz Theorem in dimension 3 using degenerations of toric varieties.
We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…
The Hodge-de Rham Theorem is introduced and discussed. This result has implications for the general study of several partial differential equations. Some propositions which have applications to the proof of this theorem are used to study…
We show the existence of Hall polynomials for representation-finite cluster-tilted algebras.
We construct a computable, computably categorical field of infinite transcendence degree over the rational numbers, using the Fermat polynomials and assorted results from algebraic geometry. We also show that this field has an intrinsically…
We identify computability-theoretic properties enabling us to separate various statements about partial orders in reverse mathematics. We obtain simpler proofs of existing separations, and deduce new compound ones. This work is part of a…
We provide a simple proof of a computable analogue to the Jayne Rogers Theorem from descriptive set theory. The difficulty of the proof is delegated to a simulation result pertaining to non-deterministic type-2 machines. Thus, we…