Related papers: Counterexamples to double recurrence for non-commu…

Let $P$ be an arbitrary partially ordered set, $R$ a commutative ring with identity and $FI(P,R)$ the finitary incidence algebra of $P$ over $R$. Under some natural assumption on $R$, we prove that each Lie-type derivation of $FI(P,R)$ is…

In this paper we study some sophisticated supercongruences involving dual sequences. For $n=0,1,2,\ldots$ define $$d_n(x)=\sum_{k=0}^n\binom nk\binom xk2^k$$ and $$s_n(x)=\sum_{k=0}^n\binom nk\binom xk\binom{x+k}k=\sum_{k=0}^n\binom…

Let a and b be non-zero rational numbers that are multiplicatively independent. We study the natural density of the set of primes p for which the subgroup of the multiplicative group of the finite field with p elements generated by (a\mod…

Deterministic two-way transducers with pebbles (aka pebble transducers) capture the class of polyregular functions, which extend the string-to-string regular functions allowing polynomial growth instead of linear growth. One of the most…

The purpose of this note is to revisit the results of arXiv:1407.4324 from a slightly different perspective, outlining how, if the integral closures of a finite set of prime ideals abide the expected convexity patterns, then the existence…

Let $ T\colon[0,1]^d\to [0,1]^d $ be a piecewise expanding map with an absolutely continuous invariant measure $ \mu $. Let $ \{H_n\} $ be a sequence of hyperrectangles or hyperboloids centered at the origin. Denote by $ \mathcal R(\{H_n\})…

Arthur Cohn's irreducibility criterion for polynomials with integer coefficients and its generalization connect primes to irreducibles, and integral bases to the variable $x$. As we follow this link, we find that these polynomials are ready…

Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often consists of two steps: first, internal measurements involving…

We identify a recursive structure among factorizations of polynomial values into two integer factors. Polynomials for which this recursive structure characterizes all non-trivial representations of integer factorizations of the polynomial…

We consider products of two Macdonald polynomials of type A, indexed by dominant weights which are respectively a multiple of the first fundamental weight and a weight having zero component on the k-th fundamental weight. We give the…

Using ideas from automata theory we design a new efficient (deterministic) identity test for the \emph{noncommutative} polynomial identity testing problem (first introduced and studied in \cite{RS05,BW05}). We also apply this idea to the…

We consider a sequence of polynomials $\{P_n\}_{n \geq 0}$ satisfying a special $R_{II}$ type recurrence relation where the zeros of $P_n$ are simple and lie on the real line. It turns out that the polynomial $P_n$, for any $n \geq 2$, is…

We consider the set $\mathcal{R}_\mathrm{io}$ of points returning infinitely many times to a sequence of shrinking targets around themselves. Under additional assumptions we improve Boshernitzan's pioneering result on the speed of…

Given a probability measure $\mu$ with infinite support on the unit circle $\partial\mathbb{D}=\{z:|z|=1\}$, we consider a sequence of paraorthogonal polynomials $\h_n(z,\lambda)$ vanishing at $z=\lambda$ where $\lambda \in \T$ is fixed. We…

In this paper we construct infinite sequences of monic irreducible polynomials with coefficients in odd prime fields by means of a transformation introduced by Cohen in 1992. We make no assumptions on the coefficients of the first…

We introduce the notion of double Courant-Dorfman algebra and prove that it satisfies the so-called Kontsevich-Rosenberg principle, that is, a double Courant-Dorfman algebra induces Roytenberg's Courant-Dorfman algebras on the affine…

Directional replicability addresses the question of whether an effect studied across $n$ independent studies is present with the same direction in at least $r$ of them, for $r \geq 2$. When the expected direction of the effect is not…

We say that a permutation $\pi=\pi_1\pi_2\cdots \pi_n \in \mathfrak{S}_n$ has a peak at index $i$ if $\pi_{i-1} < \pi_i > \pi_{i+1}$. Let $\mathcal{P}(\pi)$ denote the set of indices where $\pi$ has a peak. Given a set $S$ of positive…

We introduce and analyze a novel class of binary operations on finite-dimensional vector spaces over a field K, defined by second-order multilinear expressions with linear shifts. These operations generate polynomials whose degree increases…

We introduce a sequence $P_{2n}$ of monic reciprocal polynomials with integer coefficients having the central coefficients fixed. We prove that the ratio between number of nonunimodular roots of $P_{2n}$ and its degree $d$ has a limit when…