Related papers: $n$-valued Coset Groups and Dynamics
The problem we consider is to define families of n-dimensional integrals, endowed with group actions as in Rhin-Viola's work on irrationality measures of $\zeta(2)$ and $\zeta(3)$, the values of which are linear forms, over the rationals,…
We derive asymptotic formulae for the coefficients of bivariate generating functions with algebraic and logarithmic factors. Logarithms appear when encoding cycles of combinatorial objects, and also implicitly when objects can be broken…
Designing plausible network models typically requires scholars to form a priori intuitions on the key drivers of network formation. Oftentimes, these intuitions are supported by the statistical estimation of a selection of network evolution…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
We study Schreier dynamical systems associated with a vast family of groups that hosts many known examples of groups of intermediate growth. We are interested in the orbital graphs for the actions of these groups on $d-$regular rooted trees…
The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices (n points). In this paper, we generalize many aspects of this situation. We introduce random shifts of…
We recalculate the beta functions of higher derivative gravity in four dimensions using the one--loop approximation to an Exact Renormalization Group Equation. We reproduce the beta functions of the dimensionless couplings that were known…
In the paper, we obtain the estimates connecting codimensions of varieties of non-associative algebras and corresponding varieties of dialgebras.
The class of evolving groups is defined and investigated, as well as their connections to examples in the field of Galois cohomology. Evolving groups are proved to be Sylow Tower groups in a rather strong sense. In addition, evolving groups…
We consider the coset poset associated with the families of proper subgroups, proper subgroups of finite index, and proper normal subgroups of finite index. We investigate under which conditions those coset posets have contractible…
We consider the $q$th root number function for the symmetric group. Our aim is to develop an asymptotic formula for the multiplicities of the $q$th root number function as $q$ tends to $\infty$. We use character theory, number theory and…
We present a unified framework of combinatorial descriptions, and the analogous asymptotic growth of the coefficients of two general families of functions related to integer partitions. In particular, we resolve several conjectures and…
The aim of this work is to expose some asymptotic series associated to some expressions involving the volume of the n-dimensional unit ball. All proofs and the methods used for improving the classical inequalities announced in the final…
New asymptotic approximations of the non-central $t$ distribution are given, a generalization of the Student's $t$ distribution. Using new integral representations, we give new asymptotic expansions for large values of the noncentrality…
Continuing a well established tradition of associating convex bodies to monomial ideals, we initiate a program to construct asymptotic Newton polyhedra from decompositions of monomial ideals. This is achieved by forming a graded family of…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
We describe the geometric structures involved in the variational formulation of physical theories. In presence of these structures, the constitutive set of a physical system can be generated by a family of functions. We discuss conditions,…
We consider the structure of groups and algebras that can be represented as automorphisms or derivations of distributive products -- which includes nonassociative rings, modules, forms, and commutation of groups and nonassociative loops. In…
A general framework for the connection between characteristic formulae and behavioral semantics is described in [2]. This approach does not suitably cover semantics defined by nested fixed points, such as the n-nested simulation semantics…
We discuss representations of monogenic functions over very regular groups.