Related papers: Relating Left and Right Extensions of Maximal Repe…

The dynamical conductivity of interacting multiband electronic systems derived in Ref.[1] is shown to be consistent with the general form of the Ward identity. Using the semiphenomenological form of this conductivity formula, we have…

We find necessary and sufficient conditions for gauge invariance of the action of Double Field Theory (DFT) as well as closure of the algebra of gauge symmetries. The so-called weak and strong constraints are sufficient to satisfy them, but…

A word is called carefully synchronising for a partial deterministic finite semi-automaton if it maps all states to the same state. Equivalently, it is a composition of partial transformations equal to a constant total transformation. There…

Let G be an edge-weighted hypergraph on n vertices, m edges of size \le s, where the edges have real weights in an interval [1,W]. We show that if we can approximate a maximum weight matching in G within factor alpha in time T(n,m,W) then…

A graph $G$ is said to be $k$-extendable if every matching of size $k$ in $G$ can be extended to a perfect matching of $G$, where $k$ is a positive integer. We say $G$ is $1$-excludable if for every edge $e$ of $G$, there exists a perfect…

We study the asymptotics and fine-scale behavior of quantitative combinatorial measures of infinite words and related dynamical and algebraic structures. We construct infinite recurrent words $w$ whose complexity functions $p_w(n)$ are…

If $w=u\alpha$ for $\alpha\in \Sigma=\{1,2\}$ and $u\in \Sigma^*$, then $w$ is said to be a \textit{simple right extension}of $u$ and denoted by $u\prec w$. Let $k$ be a positive integer and $P^k(\epsilon)$ denote the set of all…

In 1959, Erd\H{o}s and Gallai showed that every $2$-connected graph $G$ contains a cycle of length at least $\frac{2|E(G)|}{|V(G)|-1}$. This result was subsequently extended to weighted graphs by Bondy and Fan in 1991. A natural local…

Two important similarity measures between sequences are the longest common subsequence (LCS) and the dynamic time warping distance (DTWD). The computations of these measures for two given sequences are central tasks in a variety of…

The anti-forcing number of a perfect matching $M$ of a graph $G$ is the minimal number of edges not in $M$ whose removal make $M$ as a unique perfect matching of the resulting graph. The anti-forcing spectrum of $G$ is the set of…

Let G be a digraph (without parallel edges) such that every directed cycle has length at least four; let $\beta(G)$ denote the size of the smallest subset X in E(G) such that $G\X$ has no directed cycles, and let $\gamma(G)$ be the number…

For a directed graph $G$ without loops or parallel edges, let $\beta(G)$ denote the size of the smallest feedback arc set, i.e., the smallest subset $X \subset E(G)$ such that $G \sm X$ has no directed cycles. Let $\gamma(G)$ be the number…

For a simple-root $\lambda$-constacyclic code $\mathcal{C}$ over $\mathbb{F}_q$, let $\langle\rho\rangle$ and $\langle\rho,M\rangle$ be the subgroups of the automorphism group of $\mathcal{C}$ generated by the cyclic shift $\rho$, and by…

Graph reordering is a powerful technique to increase the locality of the representations of graphs, which can be helpful in several applications. We study how the technique can be used to improve compression of graphs and inverted indexes.…

Letters $x$ and $y$ alternate in a word $w$ if after deleting in $w$ all letters but the copies of $x$ and $y$ we either obtain a word $xyxy\cdots$ (of even or odd length) or a word $yxyx\cdots$ (of even or odd length). A graph $G=(V,E)$ is…

We show that the compressed suffix array and the compressed suffix tree for a string of length $n$ over an integer alphabet of size $\sigma\leq n$ can both be built in $O(n)$ (randomized) time using only $O(n\log\sigma)$ bits of working…

Parsing Expression Grammars (PEGs) are a formalism that can describe all deterministic context-free languages through a set of rules that specify a top-down parser for some language. PEGs are easy to use, and there are efficient…

We investigate the large deviations of the shape of the random RSK Young diagrams associated with a random word of size $n$ whose letters are independently drawn from an alphabet of size $m=m(n)$. When the letters are drawn uniformly and…

A previous article shows that any linear height bounded normal proof of a tautology in the Natural Deduction for Minimal implicational logic $M_{\supset}$ is as huge as it is redundant. More precisely, any proof in a family of…

We study the long-term behavior of the iteration of a random map consisting of Lipschitz transformations on a compact metric space, independently and randomly selected according to a fixed probability measure. Such a random map is said to…