Related papers: Expected length of the longest common subsequence …

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,…

When considering binary strings, it's natural to wonder how many distinct subsequences might exist in a given string. Given that there is an existing algorithm which provides a straightforward way to compute the number of distinct…

Assume $X_n$ is a random sample of $n$ uniform, independent points from a triangle $T$. The longest convex chain, $Y$, of $X_n$ is defined naturally. The length $|Y|$ of $Y$ is a random variable, denoted by $L_n$. In this article, we…

Let L be an infinite regular language on a totally ordered alphabet (A,<). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically with respect to < leads to an infinite sequence over the…

Let $\A=\{a_1<a_2<a_3.....<a_n<...\}$ be an infinite sequence of integers and let $R_2(n)=|\{(i,j):\ \ a_i+a_j=n;\ \ a_i,a_j\in \A;\ \ i\le j\}|$. We define $S_k=\s_{l=1}^k(R_2(2l)-R_2(2l+1))$. We prove that, if $L^{\infty}$ norm of…

We consider the set of finite random words $\mathcal A^\star$, with independent letters drawn from a finite or infinite totally ordered alphabet according to a general probability distribution. On a specific subset of $\mathcal A^\star$,…

Any finite word $w$ of length $n$ contains at most $n+1$ distinct palindromic factors. If the bound $n+1$ is reached, the word $w$ is called rich. The number of rich words of length $n$ over an alphabet of cardinality $q$ is denoted…

We present the first $\mathrm{o}(n)$-space polynomial-time algorithm for computing the length of a longest common subsequence. Given two strings of length $n$, the algorithm runs in $\mathrm{O}(n^{3})$ time with $\mathrm{O}\left(\frac{n…

The Oldenburger-Kolakoski sequence is the only infinite sequence over the alphabet $\{1,2\}$ that starts with $1$ and is its own run-length encoding. In the present work, we take a step back from this largely known and studied sequence by…

We obtain an explicit formula for the variance of the number of $k$-peaks in a uniformly random permutation. This is then used to obtain an asymptotic formula for the variance of the length of longest $k$-alternating subsequence in random…

We prove that a random word of length $n$ over a $k$-ary fixed alphabet contains, on expectation, $\Theta(\sqrt{n})$ distinct palindromic factors. We study this number of factors, $E(n,k)$, in detail, showing that the limit…

A longest common extension (LCE) query on a string computes the length of the longest common suffix or prefix at two given positions. A dynamic LCE algorithm maintains a data structure that allows efficient LCE queries on a string that can…

We revisit, beyond the uniform case, some aspects of the convergence of the cumulative shape of the RSK Young diagrams associated with random words, obtaining rates of convergence in Kolmogorov's distance. Since the length of the top row of…

Consider two random strings having the same length and generated by an iid sequence taking its values uniformly in a fixed finite alphabet. Artificially place a long constant block into one of the strings, where a constant block is a…

We consider the number of occurrences of subwords (non-consecutive sub-sequences) in a given word. We first define the notion of subword entropy of a given word that measures the maximal number of occurrences among all possible subwords. We…

Zipf's law of abbreviation, namely the tendency of more frequent words to be shorter, has been viewed as a manifestation of compression, i.e. the minimization of the length of forms -- a universal principle of natural communication.…

We investigate the order of the variance of the optimal alignments score of two independent iid binary random words having the same length. The letters are equiprobable, but the scoring function is such that one letter has a larger score…

We study higher order convexity properties of random point sets in the unit square. Given $n$ uniform i.i.d random points, we derive asymptotic estimates for the maximal number of them which are in $k$-monotone position, subject to mild…

A famous result by Hammersley and Versik-Kerov states that the length $L_n$ of the longest increasing subsequence among $n$ iid continuous random variables grows like $2\sqrt{n}$. We investigate here the asymptotic behavior of $L_n$ for…

In combinatorics on words, a word w of length n over an alphabet of size q is said to be privileged if n <= 1 or if n >= 2 and w has a privileged border that occurs exactly twice in w. Forsyth, Jayakumar and Shallit proved that there exist…