Related papers: One-dimensional quasi-uniform Kronecker sequences

We investigate the generalized Kronecker algebra $\mathcal{K}_r = k\Gamma_r$ with $r \geq 3$ arrows. Given a regular component $\mathcal{C}$ of the Auslander-Reiten quiver of $\mathcal{K}_r$, we show that the quasi-rank $rk(\mathcal{C}) \in…

This note is motivated by an old result of Kronecker on monic polynomials with integer coefficients having all their roots in the unit disc. We call such polynomials Kronecker polynomials for short. Let $k(n)$ denote the number of Kronecker…

In 1986 A. Ancona showed, using the Koebe one-quarter Theorem, that for a simply-connected planar domain the constant in the Hardy inequality with the distance to the boundary is greater than or equal to 1/16. In this paper we consider…

We give a simple, elementary proof that a uniform algebra is weakly sequentially complete if and only if it is finite-dimensional.

We discuss when a unital homomorphism {\phi} : C(X) \rightarrow A can be approximated by finite-dimensional homomorphisms, where X is a compact metric space and A is unital simple C*-algebra with tracial rank one. In this paper, we will…

Let $H$ be a $k$-uniform hypergraph on $n$ vertices where $n$ is a sufficiently large integer not divisible by $k$. We prove that if the minimum $(k-1)$-degree of $H$ is at least $\lfloor n/k \rfloor$, then $H$ contains a matching with…

The seminal work of Kurzweil (1955) provides for any fixed badly approximable $\alpha$ and monotonically decreasing $\psi$ a Khintchine-type statement on the set of the inhomogeneous real parameters $\gamma$ for which $\lVert n \alpha +…

We give a streamlined proof of a theorem of Foxby and Halvorsen. The theorem states that certain relative K-groups made from chain complexes with bounded (but arbitrarily long) length coincide with similar K-groups in which one sets an…

We present several upper and lower bounds on the Kronecker coefficients of the symmetric group. We prove $k$-stability of the Kronecker coefficients generalizing the (usual) stability, and giving a new upper bound. We prove a lower bound…

After defining a notion of $\epsilon$-density, we provide for any real algebraic number $\alpha$ an estimate of the smallest $\epsilon$ such that for each $m>1$ the set of vectors of the form $(t,t\alpha,...,t\alpha^{m-1})$ for $t\in\R$ is…

For a closed subset $K$ of a compact metric space $A$ possessing an $\alpha$-regular measure $\mu$ with $\mu(K)>0$, we prove that whenever $s>\alpha$, any sequence of weighted minimal Riesz $s$-energy configurations…

Let $\Lambda$ be a ring and $\mathcal N$ a class of $\Lambda$-modules. A $\Lambda$-module is said to be generated by $\mathcal N$ provided that it is a factor module of a direct sum of modules in $\mathcal N$. The semi-simple…

In this paper, using the well-known Karlsson-Minton formula, we mainly establish two divisibility results concerning truncated hypergeometric series. Let $n>2$ and $q>0$ be integers with $2\mid n$ or $2\nmid q$. We show that…

Although a generic uniformly distributed sequence has Poissonian pair correlations, only one explicit example has been found up to now. Additionally, it is even known that many classes of uniformly distributed sequences, like van der Corput…

By practicing the philosophy of our beloved late master, Marco Schutzenberger, to whose memory this article is dedicated, we give an insightful bijective proof of the three-term recurrence satisfied by the Hipparchus-Schroeder numbers…

We say that a group is {\em almost abelian} if every commutator is central and squares to the identity. Now let $G$ be the Galois group of the algebraic closure of the field $\QQ$ of rational numbers in the field of complex numbers. Let…

We prove an asymptotic formula for the number of $k$-uniform hypergraphs with a given degree sequence, for a wide range of parameters. In particular, we find a formula that is asymptotically equal to the number of $d$-regular $k$-uniform…

An interesting result of Veech more than 50 years ago is a parity, or mod $2$, version of the Kronecker--Weyl equidistribution theorem concerning the irrational rotation sequence $\{q\alpha\}$, $q=0,1,2,3,\ldots.$ If $\alpha$ is badly…

Generalizing a result of \cite{Z1991, CPZ} about elliptic modular forms, we give a closed formula for the sum of all Hilbert Hecke eigenforms over a totally real number field with strict class number $1$, multiplied by their period…

We study analogues of Kronecker coefficients for symmetric inverse semigroups, for dual symmetric inverse semigroups and for the inverse semigroups of bijections between subquotients of finite sets. In all cases we reduce the problem of…