Related papers: Approximation of center-valued Betti-numbers
In this work, we determined the general terms of all almost balancing numbers of first and second type in terms of balancing numbers and conversely we determined the general terms of all balancing numbers in terms of all almost balancing…
We present an elementary proof of the generalization of the $k$-bonacci Binet formula, a closed form calculation of the $k$-bonacci numbers using the roots of the characteristic polynomial of the $k$-bonacci recursion.
A divide-and-conquer algorithm for computing the Betti numbers of finite $T_0$-spaces is presented. It extensively uses the Mayer-Vietoris sequence for open coverings. In the end, the computational costs for a parallelisation of this method…
We propose a generalisation for the notion of the centre of an algebra in the setup of algebras graded by an arbitrary abelian group G. Our generalisation, which we call the G-centre, is designed to control the endomorphism category of the…
We give a version of the Borel-Cantelli lemma. As an application, we prove an almost sure local central limit theorem. As another application, we prove a dynamical Borel-Cantelli lemma for systems with sufficiently fast decay of…
In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…
The purpose of this article is to show a close relationship between the generalized central series of Leibniz algebras. Some analogues of the classical group-theoretical theorems of Schur and Baer for Leibniz algebras are proved.
This is a sequel to arXiv:1308.3604. We study applications to limit multiplicity generalizing the results of arXiv:1208.2257.
Wolfang L\"uck asked if twisted $L^2$-Betti numbers of a group are equal to the usual $L^2$-Betti numbers rescaled by the dimension of the twisting representation. We confirm this for sofic groups.
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.
The so-called Atiyah conjecture states that the von Neumann dimensions of the L2-homology modules of free G-CW-complexes belong to a certain set of rational numbers, depending on the finite subgroups of G. In this article we extend this…
We provide a simple method to compute the Betti numbers if the Stanley-Reisner ideal of a simplicial tree and its Alexander dual.
In this paper, we study the multigraded Betti numbers of Veronese embeddings of projective spaces. Due to Hochster's formula, we interpret these multigraded Betti numbers in terms of the homology of certain simplicial complexes. By…
The purpose of this paper is to derive some identities of the higher order generalized twisted Bernoulli numbers and polynomials attached to $\chi$ from the properties of the p-adic invariant integrals.
The paper study the discrete sets of translations of the Gaussian function that span the spaces L1(R) and L2(R).
Probably we have observed a new simple phenomena dealing with approximations to two real numbers.
We derive asymptotic formulas for central extended binomial coefficients, which are generalizations of binomial coefficients. To do so, we relate the exact distribution of the sum of independent discrete uniform random variables to the…
We introduce a quantitative version of polynomial cohomology for discrete groups and show that it coincides with usual group cohomology when combinatorial filling functions are polynomially bounded. As an application, we show that Betti…
In this paper, I generalize a previous one about hilbertian kernels and approximation theory