Related papers: Insertions Yielding Equivalent Double Occurrence W…
A double occurrence word $w$ over a finite alphabet $\Sigma$ is a word in which each alphabet letter appears exactly twice. Such words arise naturally in the study of topology, graph theory, and combinatorics. Recently, double occurrence…
In the present paper we consider biologically motivated reduction operations on double occurrence words. Then we define the nesting index of a double occurrence word to be the least number of reduction operations it takes for a word to be…
The binomial notation (w u) represents the number of occurrences of the word u as a (scattered) subword in w. We first introduce and study possible uses of a geometrical interpretation of (w ab) and (w ba) when a and b are distinct letters.…
Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match or are compatible with all letters; partial words without holes are said to be full words (or simply words). Given an infinite…
When flipping a fair coin, let $W = L_1L_2...L_N$ with $L_i\in\{H,T\}$ be a binary word of length $N=2$ or $N=3$. In this paper, we establish second- and third-order linear recurrence relations and their generating functions to discuss the…
In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to avoid a pattern $p$ over an alphabet $\Delta$ if there is no factor $f$ of $w$ such that $f=h(p)$ where $h:\Delta^*\to\Sigma^*$ is a non-erasing morphism. A pattern…
Tandem duplication is an evolutionary process whereby a segment of DNA is replicated and proximally inserted. The different configurations that can arise from this process give rise to some interesting combinatorial questions. Firstly, we…
A computational model of the construction of word meaning through exposure to texts is built in order to simulate the effects of co-occurrence values on word semantic similarities, paragraph by paragraph. Semantic similarity is here viewed…
Co-occurrences between two words provide useful insights into the semantics of those words. Consequently, numerous prior work on word embedding learning have used co-occurrences between two words as the training signal for learning word…
Frobenius observed that the number of times an element of a finite group is obtained as a commutator is given by a specific combination of the irreducible characters of the group. More generally, for any word w the number of times an…
Models such as Word2Vec and GloVe construct word embeddings based on the co-occurrence probability $P(i,j)$ of words $i$ and $j$ in text corpora. The resulting vectors $W_i$ not only group semantically similar words but also exhibit a…
Hairpin completion is an abstract operation modeling a DNA bio-operation which receives as input a DNA strand $w = x\alpha y \calpha$, and outputs $w' = x \alpha y \bar{\alpha} \bar{x}$, where $\bar{x}$ denotes the Watson-Crick complement…
In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to avoid a pattern $p$ over an alphabet $\Delta$ if there is no factor $f$ of $w$ such that $f=h(p)$ where $h:\Delta^*\to\Sigma^*$ is a non-erasing morphism. A pattern…
For an arbitrary word $w$ on an alphabet, we can define the alternating symbol graph, $G(w)$, as the graph in which the edge $(a, b)$ is in $E$ iff the letters $a$ and $b$ alternate in the word $w$. A graph $G = (V, E)$ is said to be…
Word $W$ is said to encounter word $V$ provided there is a homomorphism $\phi$ mapping letters to nonempty words so that $\phi(V)$ is a substring of $W$. For example, taking $\phi$ such that $\phi(h)=c$ and $\phi(u)=ien$, we see that…
We study the way DALLE-2 maps symbols (words) in the prompt to their references (entities or properties of entities in the generated image). We show that in stark contrast to the way human process language, DALLE-2 does not follow the…
A word over an ordered alphabet is said to be clustering if identical letters appear adjacently in its Burrows-Wheeler transform. Such words are strictly related to (discrete) interval exchange transformations. We use an extended version of…
We consider the infinite one-sided sequence generated by the period-doubling substitution $\sigma(a,b)=(ab,aa)$, denoted by $\mathbb{D}$. Since $\mathbb{D}$ is uniformly recurrent, each factor $\omega$ appears infinite many times in the…
Enumerating the number of times one word occurs in another is a much-studied combinatorial subject. By utilizing a method that we call ``lexicographic extreme referencing'', we provide a formula for computing occurrences of one binary word…
The word inference problem is to determine languages such that the information on the number of occurrences of those subwords in the language can uniquely identify a word. A considerable amount of work has been done on this problem, but the…