Related papers: The Number of Distinct Subsequences of a Random Bi…
The problem of reconstructing strings from their substring spectra has a long history and in its most simple incarnation asks for determining under which conditions the spectrum uniquely determines the string. We study the problem of coded…
A new family of sequences is proposed. An example of sequence of this family is more accurately studied. This sequence is composed by the integers $n$ for which the sum of binary digits is equal to the sum of binary digits of $n^2$. Some…
It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are…
We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We…
We investigate the running sums of some well-known automatic sequences to determine whether they are synchronised.
Given an alphabet $S$, we consider the size of the subsets of the full sequence space $S^{\rm {\bf Z}}$ determined by the additional restriction that $x_i\not=x_{i+f(n)},\ i\in {\rm {\bf Z}},\ n\in {\rm {\bf N}}.$ Here $f$ is a positive,…
The partial sums of integer sequences that count the occurrences of a specific pattern in the binary expansion of positive integers have been investigated by different authors since the 1950s. In this note, we introduce generalized pattern…
Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them…
We consider procedures of sampling parts from a random integer partition. We determine asymptotically the probabilty distribution of the randomly-selected part whenever the positive integer that is partitioned becomes large.
Let us call a sequence of numbers heapable if they can be sequentially inserted to form a binary tree with the heap property, where each insertion subsequent to the first occurs at a leaf of the tree, i.e. below a previously placed number.…
We consider the problem of updating the information about multiple longest common sub-sequences. This kind of sub-sequences is used to highlight information that is shared across several information sequences, therefore it is extensively…
Let A be a set of integers dense in a finite interval. We establish upper and lower bounds for the longest regularly-spaced and convex subsets of A and of A-A.
A method for encoding and decoding spectrum shaped binary run-length constrained sequences is described. The binary sequences with predefined range of exponential sums are introduced. On the base of Cover's enumerative scheme, recurrence…
A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the…
In this paper we improve some existing results concerning the approximation of the distribution of extremes of a 1-dependent and stationary sequence of random variables. We enlarge the range of applicability and improve the approximation…
We propose novel algorithms for sequence prediction based on ideas from stringology. These algorithms are time and space efficient and satisfy mistake bounds related to particular stringological complexity measures of the sequence. In this…
We consider the degrees of the elements of a homogeneous system of parameters for the ring of invariants of a binary form, give a divisibility condition, and a complete classification for forms of degree at most 8.
We analyze complex networks under random matrix theory framework. Particularly, we show that $\Delta_3$ statistic, which gives information about the long range correlations among eigenvalues, provides a qualitative measure of randomness in…
In this paper we provide an overview of a series of recent results regarding algorithms for searching for subsequences in words or for the analysis of the sets of subsequences occurring in a word.
We study the binary Ehrenfeucht Mycielski sequence seeking a balance between the number of occurrences of different binary strings. There have been numerous attempts to prove the balance conjecture of the sequence, which roughly states that…