Related papers: A Package of Programs for Determination of Some Cl…
We present probabilistic neural programs, a framework for program induction that permits flexible specification of both a computational model and inference algorithm while simultaneously enabling the use of deep neural networks.…
Science and engineering have requests for a wide variety of programs, but I think that all of them can be divided between two groups. Programs of the first group deal with the well known situations and, by using well known equations, give…
We study the number of cylic subgroups in finite groups and get that $G$ has $|G|-3$ cyclic subgroups if and only if $G \cong D_{10}$ or $Q_8$.
We present a framework to determine subgroups of tetrahedron groups and tetrahedron Kleinian groups, based on tools in color symmetry theory.
Many different programs are the implementation of the same algorithm. The collection of programs can be partitioned into different classes corresponding to the algorithms they implement. This makes the collection of algorithms a quotient of…
We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…
We establish the Minimal Model Program for arithmetic threefolds whose residue characteristics are greater than five. In doing this, we generalize the theory of global $F$-regularity to mixed characteristic and identify certain stable…
A quantum computer can efficiently find the order of an element in a group, factors of composite integers, discrete logarithms, stabilisers in Abelian groups, and `hidden' or `unknown' subgroups of Abelian groups. It is already known how to…
We present an algorithm to explore various properties of the numerical semigroups with a given maximum primitive. In particular, we count the number of such numerical semigroups and verify that there is no counterexample to Wilf's…
We study the structure of the family of numerical semigroups with fixed multiplicity and Frobenius number. We give an algorithmic method to compute all the semigroups in this family. As an application we compute the set of all numerical…
We give several characterisations of groupoids determined by involutive automorphisms on semilattices of groups.
This paper gives a systematic construction of certain covers of finite semigroups. These covers will be used in future work on the complexity of finite semigroups.
The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
We give a general constructive proof for hierarchical coordinatizations (Lagrange Decompositions) of permutation groups. The generalization originates from the investigation of how the subgroup chains of finite permutation groups yield…
We classify the thick subcategories of an algebraic triangulated standard category with finitely many indecomposable objects.
We present a family of non-abelian groups for which the hidden subgroup problem can be solved efficiently on a quantum computer.
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
A program is a finite piece of data that produces a (possibly infinite) sequence of primitive instructions. From scratch we develop a linear notation for sequential, imperative programs, using a familiar class of primitive instructions and…
For a prime $p$, we describe a protocol for handling a specific type of fusion system on a $p$-group by computer. These fusion systems contain all saturated fusion systems. This framework allows us to computationally determine whether or…