相关论文: Algebraic independence of sequences generated by (…

In this work we present the computer algebra package HarmonicSums and its theoretical background for the manipulation of harmonic sums and some related quantities as for example Euler-Zagier sums and harmonic polylogarithms. Harmonic sums…

We derive the algebraic relations of alternating and non-alternating finite harmonic sums up to the sums of depth~6. All relations for the sums up to weight~6 are given in explicit form. These relations depend on the structure of the index…

The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index calss…

Symmetric homology is an analog of cyclic homology in which the cyclic groups are replaced by symmetric groups. The foundations for the theory of symmetric homology of algebras are developed in the context of crossed simplicial groups using…

A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating…

The cyclotomic matrix is commonly used to arrange cyclotomic numbers in a convenient format. A natural question is whether the structure of the matrix can reflect properties of these numbers. In this article, we examine cyclotomic numbers…

The purpose of this article is to show that the bivariant algebraic $A$-cobordism groups considered previously by the author are independent of the chosen base ring $A$. This result is proven by analyzing the bivariant ideal generated by…

Subobject independence as morphism co-possibility has recently been defined in [2] and studied in the context of algebraic quantum field theory. This notion of independence is handy when it comes to systems coming from physics, but when…

In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…

The paper studies algebraic independence of certain reciprocal sums of Fibonacci and Lucas sequences. Also more general binary recurrences are considered. The main tool is Mahler's method reducing the investigation of the algebraic…

We define a new basis of the algebra of quasi-symmetric functions by lifting the cycle-index polynomials of symmetric groups to noncommutative polynomials with coefficients in the algebra of free quasi-symmetric functions, and then…

The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin…

We give conditions on a finite set of series of rational numbers to ensure that they are algebraically independent. Specialising our results to polynomials of lower degree, we also obtain new results on irrationality and $mathbb{Q}$-linear…

We consider nested sums involving the Pochhammer symbol at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi,$ $\log(2)$ or zeta values. In order to perform these simplifications, we view the series as…

We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of…

Hazewinkel proved the Ditters conjecture that the algebra of quasisymmetric functions over the integers is free commutative by constructing a nice polynomial basis. In this paper we prove a structure theorem for the algebra of peak…

Usually creative telescoping is used to derive recurrences for sums. In this article we show that the non-existence of a creative telescoping solution, and more generally, of a parameterized telescoping solution, proves algebraic…

This paper introduces an analogue of the Solomon descent algebra for the complex reflection groups of type $G(r,1,n)$. As with the Solomon descent algebra, our algebra has a basis given by sums of `distinguished' coset representatives for…

This paper is concerned with the axiomatic basis of structures within Hypercompositional Algebra. It is proven that the axioms employed in the definition of numerous hypercompositional structures lack independence. Accordingly, novel…

We develop a theory of formal multivariate polynomials over commutative rings by treating them as ring terms. Our main result is that two ring terms are s-equivalent (when expanded they yield the same standard polynomial) iff they are…