相关论文: Sequence pairs with asymptotically optimal aperiod…

We show that sequences of the form $\alpha n^{\theta} \pmod{1}$ with $\alpha > 0$ and $0 < \theta < \tfrac{43}{117} = \tfrac{1}{3} + 0.0341 \ldots$ have Poissonian pair correlation. This improves upon the previous result by Lutsko,…

We consider sequences of the form $\left(a_{n} \alpha\right)_{n}$ mod 1, where $\alpha\in\left[0,1\right]$ and where $\left(a_{n}\right)_{n}$ is a strictly increasing sequence of positive integers. If the asymptotic distribution of the pair…

The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a property has a small witness, i.e. a witness in every definable…

The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…

We study systems of globally coupled interval maps, where the identical individual maps have two expanding, fractional linear, onto branches, and where the coupling is introduced via a parameter - common to all individual maps - that…

In this paper, we study the power and limitations of computing effectively generic sequences using effectively random oracles. Previously, it was known that every 2-random sequence computes a 1-generic sequence (as shown by Kautz) and every…

This paper addresses the qualitative theory of mixed-order positive linear coupled systems with bounded or unbounded delays. First, we introduce a general result on the existence and uniqueness of solutions to mixed-order linear coupled…

In this paper, we prove an asymptotic formula for the number of relatively prime pairs in the Piatetski-Shapiro sequence of arbitrarily large order. This improves the result of Pimsert, Srichan and Tangsupphathawat (2023), the order of…

A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…

In our problem, we are given access to a number of sequences of nonnegative i.i.d. random variables, whose realizations are observed sequentially. All sequences are of the same finite length. The goal is to pick one element from each…

The distribution of differences of consecutive members of sequences of primes is investigated. A quantitative measure for oscillations among these differences is the curvature of the sequence. If the sequence is not too sparse, then sharp…

The accurate classification of galaxies in large-sample astrophysical databases of galaxy clusters depends sensitively on the ability to distinguish between morphological types, especially at higher redshifts. This capability can be…

We show that the closure of the value set of a real linear recurrence sequence is the union of a countable set and a finite collection of intervals. Conversely, any finite collection of closed intervals is the closure of the value set of…

We study ratio limits of the consecutive terms of weighted $n$-generalized Fibonacci sequences generated from arbitrary complex initial conditions by linear recurrences with arbitrary complex weights. We prove that if the characteristic…

The problem as to when two noncommuting observables are considered to have the same value arises commonly, but shows a nontrivial difficulty. Here, an answer is given by establishing the notion of perfect correlations between noncommuting…

We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…

In this article we study the pair correlation statistic for higher dimensional sequences. We show that for any $d\geq 2$, strictly increasing sequences $(a_n^{(1)}),\ldots, (a_n^{(d)})$ of natural numbers have metric Poissonian pair…

The repetition threshold of a class of sequences is the smallest number $r$ such that a sequence from the class contains no repetition with exponent $> r$. We focus on the class $\mathcal{C}_d$ of $d$-ary sequences rich in palindromes. In…

We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…

We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…