Related papers: Kolakoski Sequence: Links between Recurrence, Symm…
Binary Sidel'nikov-Lempel-Cohn-Eastman sequences (or SLCE sequences) over F 2 have even period and almost perfect autocorrelation. However, the evaluation of the linear complexity of these sequences is really difficult. In this paper, we…
The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication scenario where the sender transmits a codeword from some codebook and the receiver obtains multiple noisy reads of the codeword. The common…
An infinite binary sequence has randomness rate at least $\sigma$ if, for almost every $n$, the Kolmogorov complexity of its prefix of length $n$ is at least $\sigma n$. It is known that for every rational $\sigma \in (0,1)$, on one hand,…
A look-and-say sequence is obtained iteratively by reading off the digits of the current value, grouping identical digits together: starting with 1, the sequence reads: 1, 11, 21, 1211, 111221, 312211, etc. (OEIS A005150). Starting with any…
We study the entropy $S$ of longest increasing subsequences (LIS), i.e., the logarithm of the number of distinct LIS. We consider two ensembles of sequences, namely random permutations of integers and sequences drawn i.i.d.\ from a limited…
We take under consideration Young measures with densities. The notion of density of a Young measure is introduced and illustrated with examples. It is proved that the density of a Young measure is weakly sequentially closed set. In the case…
In this paper, we give the explicit bounds for the data of objects involved in some basic theorems of Singularity theory: the Inverse, Implicit and Rank Theorems for Lipschitz mappings, Splitting Lemma and Morse Lemma, the density and…
In this paper we consider the problem of encoding data into \textit{repeat-free} sequences in which sequences are imposed to contain any $k$-tuple at most once (for predefined $k$). First, the capacity of the repeat-free constraint are…
An inversion sequence of length $n$ is an integer sequence $e=e_{1}e_{2}\dots e_{n}$ such that $0\leq e_{i}<i$ for each $i$. Corteel--Martinez--Savage--Weselcouch and Mansour--Shattuck began the study of patterns in inversion sequences,…
We consider the number of blocks involved in the last merger of a $\Lambda$-coalescent started with $n$ blocks. We give conditions under which, as $n \to \infty$, the sequence of these random variables a) is tight, b) converges in…
Let $\Sigma$ be a countable alphabet. For $r\geq 1$, an infinite sequence $s$ with characters from $\Sigma$ is called $r$-quasi-regular, if for each $\sigma\in\Sigma$ the ratio of the longest to shortest interval between consecutive…
This paper provides a unified framework connecting dynamical systems with tools from topological data analysis and geometric topology and inspires new interactions among dynamical systems, topology, and nonlinear analysis. To this end, we…
We give recurrences, generating functions and explicit exact expressions for the enumeration of fundamental quantities involving runs in binary strings. We first focus on enumerations concerning runs of ones, and we then analyse the same…
The results of Bergelson-Host-Kra and Leibman say that a multiple polynomial correlation sequence can be decomposed into a sum of a nilsequence (a sequence defined by evaluating a continuous function along an orbit in a nilsystem) and a…
We consider an ensemble of $N$ discrete nonintersecting paths starting from equidistant points and ending at consecutive integers. Our first result is an explicit formula for the correlation kernel that allows us to analyze the process as…
In this paper, the two settings we are concerned with are $\Gamma < \operatorname{SO}(n, 1)$ a Zariski dense Schottky semigroup and $\Gamma < \operatorname{SL}_2(\mathbb C)$ a Zariski dense continued fractions semigroup. In both settings,…
A set of sequences is said to converge simultaneously if there exists an infinite subset $H$ of the index set $\omega$ such that all sequences converge when restricted to $H$. We discuss simultaneous convergence of sequences in the same or…
We exhibit the densest sequence on the unit circle R/Z, x_k= log(2k-1)/log(2) (mod 1).
In this article we correct the proof of a uniqueness result for self-similar solutions to Smoluchowski's coagulation equation for kernels $K=K(x,y)$ that are homogeneous of degree zero and close to constant in the sense that…
Let $G$ be a finite $D$-quasirandom group and $A \subset G^{k}$ a $\delta$-dense subset. Then the density of the set of side lengths $g$ of corners \[ \{(a_{1},\dots,a_{k}),(ga_{1},a_{2},\dots,a_{k}),\dots,(ga_{1},\dots,ga_{k})\} \subset A…