Related papers: GAP Computations Concerning Probabilistic Generati…
This note deals with the computation of the factorization number $F_2(G)$ of a finite group $G$. By using the M\"{o}bius inversion formula, explicit expressions of $F_2(G)$ are obtained for two classes of finite abelian groups, improving…
The aim of this thesis is to determine classes of NP relations for which random generation and approximate counting problems admit an efficient solution. Since efficient rank implies efficient random generation, we first investigate some…
This paper investigates the usage of generating functions (GFs) encoding measures over the program variables for reasoning about discrete probabilistic programs. To that end, we define a denotational GF-transformer semantics for…
We determine for which known finite simple groups $G$ and which primes $p$ the $p$-fusion system of $G$ is simple. This means first collecting together the results that were already known (and correcting two errors made in an earlier study…
Random number generators are widely used in practical algorithms. Examples include simulation, number theory (primality testing and integer factorization), fault tolerance, routing, cryptography, optimization by simulated annealing, and…
It is well known that every finite simple group has a generating pair. Moreover, Guralnick and Kantor proved that every finite simple group has the stronger property, known as $\frac{3}{2}$-generation, that every nontrivial element is…
In this paper we define Ordered Generating System for finite non-abelian groups, which is a generalization of the basis theorem for finite abelian groups. We prove the following: If each composition factor of a group G has Ordered…
Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose…
In this paper, we introduce a novel approach for generating random elements of a finite group given a set of generators of that. Our method draws upon combinatorial group theory and automata theory to achieve this objective. Furthermore, we…
Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…
We consider the random hypergraph on a finite vertex set by choosing each set of vertices as an hyperedge independently at random. We express the probability distributions of the (lower-)associated simplicial complex and the…
Generative probabilistic forecasting produces future time series samples according to the conditional probability distribution given past time series observations. Such techniques are essential in risk-based decision-making and planning…
There has been considerable interest in recent decades in questions of random generation of finite and profinite groups, and finite simple groups in particular. In this paper we study similar notions for finite and profinite associative…
Motivated by the theory of Riemann surfaces, we classify all possibilities for finite simple groups acting faithfully on a compact Riemann surface of genus at least 2 in such a way that all non-trivial elements have at most three fixed…
Let $G$ be a finite simple group. In this paper we consider the existence of small subsets $A$ of $G$ with the property that, if $y \in G$ is chosen uniformly at random, then with high probability $y$ invariably generates $G$ together with…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Bayesian nonparametric mixtures and random partition models are powerful tools for probabilistic clustering. However, standard independent mixture models can be restrictive in some applications such as inference on cell lineage due to the…
Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…
A group is $\frac{3}{2}$-generated if every non-identity element is contained in a generating pair. A conjecture of Breuer, Guralnick and Kantor from 2008 asserts that a finite group is $\frac{3}{2}$-generated if and only if every proper…
In this notes we give details of the proofs performed with GAP of the theorems of our paper "Pointed Hopf Algebras over the Sporadic Simple Groups".