Related papers: On the realization of double occurrence words

It has recently been shown in [\emph{Discrete Appl. Math.} {\bf 366} (2025) 75--85] that the resonance graph of a plane elementary bipartite graph $G$ is a daisy cube if and only if $G$ is peripherally 2-colorable. Let $G$ be a peripherally…

We obtain an explicit characterization of the stable points of the action of G=SL(2,C) on the cartesian product G^n by simultaneous conjugation on each factor, in terms of the corresponding invariant functions, and derive from it a simple…

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…

In this paper, we study some new factorizations of period-doubling sequences over a $k$-letter alphabet, where $k\geq 2$. First, we define the combinatorial and arithmetic properties of these sequences. Then, we define the kernel words of…

Let A and B be finite dimensional simple real algebras with division gradings by an abelian group G. In this paper we give necessary and sufficient conditions for the coincidence of the graded identities of A and B. We also prove that every…

The decision problems on matrices were intensively studied for many decades as matrix products play an essential role in the representation of various computational processes. However, many computational problems for matrix semigroups are…

Let $G$ be an intersection graph of $n$ geometric objects in the plane. We show that a maximum matching in $G$ can be found in $O(\rho^{3\omega/2}n^{\omega/2})$ time with high probability, where $\rho$ is the density of the geometric…

We find solutions of the six-dimensional maximal supergravity by adding a perturbation of vector fields to the solution AdS${}_3$ $\times$ S${}^3$. For certain perturbations the solution represents a dual description of an ${\cal N}=(4,0)$…

We present a sequent calculus for abstract focussing, equipped with proof-terms: in the tradition of Zeilberger's work, logical connectives and their introduction rules are left as a parameter of the system, which collapses the synchronous…

In this paper, we define a new realizability semantics for the simply typed lambda-mu-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. We also prove a completeness result of our realizability…

The complete double vertex graph $M_2(G)$ of $G$ is defined as the graph whose vertices are the $2$-multisubsets of $V(G)$, and two of such vertices are adjacent in $M_2(G)$ if their symmetric difference (as multisets) is a pair of adjacent…

The free space diagram is a popular tool to compute the well-known Fr\'echet distance. As the Fr\'echet distance is used in many different fields, many variants have been established to cover the specific needs of these applications. Often,…

The set $S_{\{i,j\}_{n}^{m}}=\{0,1,2,\ldots,m-1,m,m,m+1,\ldots,n-1,n\}\setminus\{i,j\},\quad 0<i<j\leqslant n$, is called Laplacian realizable if there exists a simple connected graph $G$ whose Laplacian spectrum is $S_{\{i,j\}_{n}^{m}}$.…

In this paper, we prove the following. First, every square matrix whose entries are multivariable rational functions over a field $\mathbb{F}$ has a Bessmertny\u{i} realization, i.e., is the Schur complement of an affine linear square…

This article focuses on subset reachability in synchronizing automata. First, we provide families of synchronizing automata with subsets which cannot be reached with short words. These families do not fulfil Don's Conjecture about subset…

Let S be a closed surface of genus at least 2. We show that a finitely generated group G which is an extension of the fundamental group H of S is word hyperbolic if and only the orbit map of the quotient group G/H on the complex of curves…

Let X be a non-empty finite set, E be a finite dimensional euclidean vector space and G a finite subgroup of O(E), the orthognal group of E. Suppose GG={U_i | i in X} is a finite set of linear lines in E and an orbit of G on which its…

In this paper three notions of emergent geometry arising from the study of gauge/gravity duals are discussed. The unifying theme behind these notions of emergent geometry is that one can derive properties of the effective action of a probe…

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…

A graph is word-representable if it can be represented in a certain way using alternation of letters in words. Word-representable graphs generalise several important and well-studied classes of graphs, and they can be characterised by…