Continuous maps with the disjoint support property

Periodica Mathematica Hungarica - It is well known that for each $$n\ge 0$$ , there is a continuous map $$ f :S^{n}\rightarrow \partial \bigtriangleup ^{n+1}$$ with the disjoint support property....     

Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic

Semigroup Forum - Let $$f_1(n), \ldots , f_k(n)$$ be polynomial functions of n. For fixed $$n\in \mathbb {N}$$ , let $$S_n\subseteq \mathbb {N}$$ be the numerical semigroup generated by...     

Menon-type identities with respect to sets of units

The Ramanujan Journal - Let $$n\ge 1$$ and let $$\mathbb {Z}_n^\star $$ be the group of units in the ring of residual classes modulo n, let $$m\ge 0$$ , $$k\ge 0$$ , $$m+k\ge 1$$ , $$u_1,\ldots...     

The pure cactus group is residually nilpotent

We show that for each $$n\in {\mathbb {N}}$$ the pure cactus group $$\Gamma _{n+1}$$ embeds into a right-angled Coxeter group and, therefore, is residually nilpotent. In addition, we construct an explicit residually torsion-free nilpotent subgroup of finite index in $$\Gamma _{n+1}$$ .     

Inequalities for the overpartition function

The Ramanujan Journal - Let $$\overline{p}(n)$$ denote the overpartition function. Engel showed that for $$n\ge 2$$ , $$\overline{p}(n)$$ satisfy the Turán inequalities, that is,...     

Extremal Betti numbers of edge ideals

Archiv der Mathematik - Let A be an algebra over a field F of characteristic zero. For every $$n\ge 1$$ , let $$\delta _n(A)$$ be the number of linearly independent multilinear proper central...     

An exponential Diophantine equation related to the sum of powers of two consecutive terms of a Lucas sequence and x-coordinates of Pell equations

Periodica Mathematica Hungarica - For the Fibonacci sequence the identity $$F_n^2+F_{n+1}^2 = F_{2n+1}$$ holds for all $$n \ge 0$$ . Let $${\mathcal {X}}:= (X_\ell )_{\ell \ge 1}$$ be the sequence...     

Spectral symmetry in conference matrices

Designs, Codes and Cryptography - A conference matrix of order n is an $$n\times n$$ matrix C with diagonal entries 0 and off-diagonal entries $$\pm 1$$ satisfying $$CC^\top =(n-1)I$$ . If C is...     

A note on polydegree (n, 1) rational inner functions,slice matrices,and singularities

Archiv der Mathematik - We analyze certain compositions of rational inner functions in the unit polydisk $$\mathbb {D}^{d}$$ with polydegree (n, 1), $$n\in \mathbb {N}^{d-1}$$ , and...     

SPECTRAL PROPERTY OF CERTAIN MORAN MEASURES IN $\mathbb{R}^{n}$ R n

Acta Mathematica Hungarica - Let $$R_k = {\rm diag}(r_{k,1}, r_{k,2}, \ldots, r_{k,n})$$ be the $$n \times n$$ expanding integer diagonal matrix, and let $$D_k\subset \mathbb Z^{n}$$ . We show that...     

On a conjecture on shifted primes with large prime factors

Archiv der Mathematik - Let $$\mathcal {P}$$ be the set of all primes and $$\pi (x)$$ be the number of primes up to x. For any $$n\ge 2$$ , let $$P^+(n)$$ be the largest prime factor of n. For...     

On the arithmetic mean of the size of cross-union families

Acta Mathematica Hungarica - Let $$n > k > 1$$ be integers, $$[n] = \{1, \ldots, n\}$$ the standard $$n$$ -element set and $${[n]\choose k}$$ the collection of all its $$k$$ -subsets....     

Asymptotics of the Number of Threshold Functions and the Singularity Probability of Random {±1}-Matrices

Doklady Mathematics - Two results concerning the number $$P(2,n)$$ of threshold functions and the singularity probability $${{\mathbb{P}}_{n}}$$ of random ( $$n \times n$$ ) $${\text{\{ }} \pm...     

Universal Relations in Asymptotic Formulas for Orthogonal Polynomials

Functional Analysis and Its Applications - Orthogonal polynomials $$P_{n}(\lambda)$$ are oscillating functions of $$n$$ as $$n\to\infty$$ for $$\lambda$$ in the absolutely continuous spectrum of...     

The extension of the $$D(-k)$$ D ( - k ) -pair $$\{k,k+1\}$$ { k,k + 1 } to a quadruple

Periodica Mathematica Hungarica - Let $$n\ne 0$$ be an integer. A set of m distinct positive integers $$\{a_1,a_2,\ldots ,a_m\}$$ is called a D(n)-m-tuple if $$a_ia_j + n$$ is a perfect square for...     

Hyperbolic spaces,principal series,and $${\mathrm{O}}(2,\infty )$$O(2,∞)

We prove that there exists no irreducible representation of the identity component of the isometry group $${\mathrm{PO}}(1,n)$$ of the real hyperbolic space of dimension n into the group $${\mathrm{O}}(2,\infty )$$ if $$n\ge 3$$. This is motivated by the existence of irreducible representations (arising from the spherical principal series) of $${\mathrm{PO}}(1,n)^{\circ }$$ into the groups $${\mathrm{O}}(p,\infty )$$ for other values of p.     

Normal pairs of noncommutative rings

This paper extends the concept of a normal pair from commutative ring theory to the context of a pair of (associative unital) rings. This is done by using the notion of integrality introduced by Atterton. It is shown that if $$R \subseteq S$$ are rings and $$D=(d_{ij})$$ is an $$n\times n$$ matrix with entries in S, then D is integral (in the sense of Atterton) over the full ring of $$n\times n$$ matrices with entries in R if and only if each $$d_{ij}$$ is integral over R. If $$R \subseteq S$$ are rings with corresponding full rings of $$n\times n$$ matrices $$R_n$$ and $$S_n$$, then $$(R_n,S_n)$$ is a normal pair if and only if (R, S) is a normal pair. Examples are given of a pair $$(\Lambda , \Gamma )$$ of noncommutative (in fact, full matrix) rings such that $$\Lambda \subset \Gamma $$ is (resp., is not) a minimal ring extension; it can be further arranged that $$(\Lambda , \Gamma )$$ is a normal pair or that $$\Lambda \subset \Gamma $$ is an integral extension.     

Estimates of Derivatives in Sobolev Spaces in Terms of Hypergeometric Functions

Mathematical Notes - The paper deals with sharp estimates of derivatives of intermediate order $$k\le n-1$$ in the Sobolev space $$\mathring W^n_2[0;1]$$ , $$n\in\mathbb N$$ . The functions...     

On generalized square-full numbers in an arithmetic progression

Czechoslovak Mathematical Journal - Let a and $$b \in \mathbb{N}$$ . Denote by Ra,b the set of all integers n > 1 whose canonical prime representation $$n = p_1^{{\alpha _1}}p_2^{{\alpha...