相关论文: On connection between division sequences and prese…
In this note we study the logarithmic derivation module of a non-free arrangement. We prove a generalized addition theorem for all arrangements. This addition theorem allows us to find various relationships between non-free arrangements,…
The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…
We find the group of equivalence transformations for equations of the form $y''= A(x)y' + F(y),$ where $A$ and $F$ are arbitrary functions. We then give a complete group classification of these families of equations, using a direct method…
Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…
We introduce and characterise grid classes, which are natural generalisations of other well-studied permutation classes. This characterisation allows us to give a new, short proof of the Fibonacci dichotomy: the number of permutations of…
The method of brackets is a method for the evaluation of definite integrals based on a small number of rules. This is employed here for the evaluation of Mellin-Barnes integral. The fundamental idea is to transform these integral…
A theory of higher colimits over categories of free presentations is developed. It is shown that different homology functors such as Hoshcshild and cyclic homology of algebras over a field of characteristic zero, simplicial derived…
A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for theevaluation of Feynman diagrams. We describe the operational rules and illustrate the method…
An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.
In general, representations of interval orders may use an arbitrary set of interval lengths. We can define subclasses of interval orders by restricting the allowable lengths of intervals. Motivated by a recent paper of Keller, Trenk, and…
This paper is devoted to the investigation of the property of order separability for free products of groups.
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
Based on Bergman's Lemma on centralizers, we obtain a sharp lower degree bound for nonconstant elements in a subalgebra generated by two elements of a free associative algebra over an arbitrary field.
In a recent article we introduced a mechanism for producing a presentation of the descent algebra of the symmetric group as a quiver with relations, the mechanism arising from a new construction of the descent algebra as a homomorphic image…
In this paper we give a precise estimate of the discrepancy of a class of uniformly distributed sequences of partitions. Among them we found a large class having low discrepancy (which means of order 1/N. One of them is the…
In this work the author studies the property close to property of order separability.
The object of observation in present paper is statistical independence of real sequences and its description as independence with re spect to certain class of densities.
In this article we give a concept of ground subgroup for finite and countable groups. By our definition such a subgroup of a group depends on a given subset of the group and on a given partition of the subset. For finite and free groups we…
This paper introduces a general method for the exploration of equivalence classes in the input space of Transformer models. The proposed approach is based on sound mathematical theory which describes the internal layers of a Transformer…
We introduce and study the concept of cyclicity degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. An…