相关论文: The Shortest Interesting Binary Words
The work takes another look at the number of runs that a string might contain and provides an alternative proof for the bound. We also propose another stronger conjecture that states that, for a fixed order on the alphabet, within every…
We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…
We consider a type of long-range percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word…
We prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open problems. These results, coming from areas such as extremal graph theory, Ramsey theory and additive…
We introduce the $k$-bonacci polyominoes, a new family of polyominoes associated with the binary words avoiding $k$ consecutive $1$'s, also called generalized $k$-bonacci words. The polyominoes are very entrancing objects, considered in…
Two finite words $u$ and $v$ are called Abelian equivalent if each letter occurs equally many times in both $u$ and $v$. The abelian closure $\mathcal{A}(\mathbf{x})$ of (the shift orbit closure of) an infinite word $\mathbf{x}$ is the set…
A prefix normal word is a binary word with the property that no substring has more $1$s than the prefix of the same length. By proving that the set of prefix normal words is a bubble language, we can exhaustively list all prefix normal…
The Shortest Common Supersequence problem (SCS for short) consists in finding a shortest common supersequence of a finite set of words on a fixed alphabet Sigma. It is well-known that its decision version denoted [SR8] in [Garey and…
The complement $\overline{x}$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. We study infinite binary words $\bf w$ that avoid sufficiently large complementary factors; that is, if $x$ is a factor of…
The \v{C}ern\'y conjecture states that every $n$-state synchronizing automaton has a reset word of length at most $(n-1)^2$. We study the hardness of finding short reset words. It is known that the exact version of the problem, i.e.,…
The block reversal of a word $w$, denoted by $\mathtt{BR}(w)$, is a generalization of the concept of the reversal of a word, obtained by concatenating the blocks of the word in the reverse order. We characterize non-binary and binary words…
There are many randomness notions. On the classical account, many of them are about whether a given infinite binary sequence is random for some given probability. If so, this probability turns out to be the same for all these notions, so…
We consider the following novel variation on a classical avoidance problem from combinatorics on words: instead of avoiding repetitions in all factors of a word, we avoid repetitions in all factors where each individual factor is considered…
Two words $w_1$ and $w_2$ are said to be $k$-binomial equivalent if every non-empty word $x$ of length at most $k$ over the alphabet of $w_1$ and $w_2$ appears as a scattered factor of $w_1$ exactly as many times as it appears as a…
A Lyndon word is a primitive string which is lexicographically smallest among cyclic permutations of its characters. Lyndon words are used for constructing bases in free Lie algebras, constructing de Bruijn sequences, finding the…
We show that there are infinitely many binary strings z, such that the sum of the on-line decision complexity of predicting the even bits of z given the previous uneven bits, and the decision complexity of predicting the uneven bits given…
In this paper, we determine the dimensions of the residue codes of extremal Type II Z4-codes for lengths 32 and 40. We demonstrate that every binary doubly even self-dual code of length 32 can be realized as the residue code of some…
Prefix normal words are binary words in which each prefix has at least the same number of $\so$s as any factor of the same length. Firstly introduced by Fici and Lipt\'ak in 2011, the problem of determining the index of the prefix…
A shuffle square is a word consisting of two shuffled copies of the same word. For instance, the Turkish word $\mathtt{\color{red}{ik}\color{blue}{i}\color{red}{li}\color{blue}{kli}}$ (binary in English) is a shuffle square, as it can be…
Large bilingual parallel texts (also known as bitexts) are usually stored in a compressed form, and previous work has shown that they can be more efficiently compressed if the fact that the two texts are mutual translations is exploited.…