Related papers: On Searching Zimin Patterns

We study a class of finite state machines, called \defi{$w$-matching machines}, which yield to simulate the behavior of pattern matching algorithms while searching for a pattern $w$. They can be used to compute the asymptotic speed, i.e.…

We study permutation (jumbled/Abelian) pattern matching over a general alphabet $\Sigma$. Given a pattern P of length m and a text T of length n, the classical task is to decide whether T contains a length-m substring whose Parikh vector…

The sequence of partial sums of Fibonacci numbers, beginning with $2$, $4$, $7$, $12$, $20$, $33,\dots$, has several combinatorial interpretations (OEIS A000071). For instance, the $n$-th term in this sequence is the number of length-$n$…

Networks are used as highly expressive tools in different disciplines. In recent years, the analysis and mining of temporal networks have attracted substantial attention. Frequent pattern mining is considered an essential task in the…

Let $k\ge 1$ be an integer, and let $P= (f_1(x), \ldots, f_k(x) )$ be $k$ admissible linear polynomials over the integers, or \textit{the pattern}. We present two algorithms that find all integers $x$ where $\max{ \{f_i(x) \} } \le n$ and…

Pattern matching with wildcards is the problem of finding all factors of a text $t$ of length $n$ that match a pattern $x$ of length $m$, where wildcards (characters that match everything) may be present. In this paper we present a number…

Strings in the real world are often encoded with some level of uncertainty. In the character-level uncertainty model, an uncertain string $X$ of length $n$ on an alphabet $\Sigma$ is a sequence of $n$ probability distributions over…

We present a new approach to the problem of enumerating permutations of length n that avoid a fixed consecutive pattern of length m. We use this idea to give explicit upper and lower bounds on the number of permutations avoiding a pattern…

The problem of ranking can be described as follows. We have a set of combinatorial objects $S$, such as, say, the k-subsets of n things, and we can imagine that they have been arranged in some list, say lexicographically, and we want to…

Fibonacci word is the archetype of the Sturmian word, and it is one of the most studied of combinatorics on words. We studied the properties of the Fibonacci word and found its density for limited value then by calculating the limit…

We show how to enumerate words in $1^{m_1} \dots n^{m_n}$ that avoid the increasing consecutive pattern $12 \dots r$ for any $r \geq 2$. Our approach yields an $O(n^{s+1})$ algorithm to enumerate words in $1^s \dots n^s$, avoiding the…

Recently, Brualdi and Cao studied $I_k$-avoiding $(0,1)$-matrices by decomposing them into zigzag paths and proved that the maximum number of $1$'s in such a matrix is given by an exact formula. We further study the structure of maximal…

A pattern $\alpha$ is a string of variables and terminal letters. We say that $\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $\alpha$ by terminal words. The matching…

In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to avoid a pattern $p$ over an alphabet $\Delta$ of variables if there is no factor $f$ of $w$ such that $f=h(p)$ where $h:\Delta^*\to\Sigma^*$ is a non-erasing…

A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present an…

The problem of frequent pattern mining has been studied quite extensively for various types of data, including sets, sequences, and graphs. Somewhat surprisingly, another important type of data, namely rank data, has received very little…

We introduce a new metric of match, called Cartesian tree matching, which means that two strings match if they have the same Cartesian trees. Based on Cartesian tree matching, we define single pattern matching for a text of length n and a…

We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…

We find finite-state recurrences to enumerate the words on the alphabet $[n]^r$ which avoid the patterns 123 and $1k(k-1)\dots2$, and, separately, the words which avoid the patterns 1234 and $1k(k-1)\dots2$.

Let $X=X(n,q)$ be the set of $n\times n$ Hermitian matrices over $\mathbb{F}_{q^2}$. It is well known that $X$ gives rise to a metric translation association scheme whose classes are induced by the rank metric. We study $d$-codes in this…