Related papers: The non-abelian squares are not context-free
For a language $L$, we consider its cyclic closure, and more generally the language $C^k(L)$, which consists of all words obtained by partitioning words from $L$ into $k$ factors and permuting them. We prove that the classes of ET0L and…
The aim of this paper is to explore non-abelian extensions of Bol algebras and to study the extensibility of a pair of automorphisms within these non-abelian extensions. We begin by researching non-abelian extensions of Bol algebras and…
We study surface links whose link groups are free abelian, and construct various stimulating and highly non-trivial examples of such surface links.
The paper is about a class of languages that extends context-free languages (CFL) and is stable under shuffle. Specifically, we investigate the class of partially-commutative context-free languages (PCCFL), where non-terminal symbols are…
We provide examples of finite non-abelian groups acting on non-trivial Severi-Brauer surfaces.
We give an example of a regular and complete subalgebra of a Cohen algebra which is not Cohen.
Non(anti)commutativity in an open free superstring and also one moving in a background anti-symmetric tensor field is investigated. In both cases, the non(anti)commutativity is shown to be a direct consequence of the non-trivial boundary…
Let $G$ be a finitely generated group, $A$ a finite set of generators and $K$ a subgroup of $G$. We call the pair $(G,K)$ context-free if the set of all words over $A$ that reduce in $G$ to an element of $K$ is a context-free language. When…
By strengthening known results about primitivity-blocking words in free groups, we prove that for any nontrivial element w of a free group of finite rank, there are words that cannot be subwords of any cyclically reduced automorphic image…
The non-Abelian aether-like Lorentz-breaking term, involving triple and quartic self-coupling vertices, is generated from the non-Abelian generalization of the Lorentz-breaking extended QED including only a minimal spinor-vector…
We show that free objects on sets do not exist in the category $bal$ of bounded archimedean $\ell$-algebras. On the other hand, we introduce the category of weighted sets and prove that free objects on weighted sets do exist in $bal$. We…
We characterize the squares occurring in infinite overlap-free binary words and construct various alpha power-free binary words containing infinitely many overlaps.
We introduce an algebraic structure for studying state-independent contextuality arguments, a key form of quantum non-classicality exemplified by the well-known Peres-Mermin magic square, and used as a source of quantum advantage. We…
We extend a conjecture of Kimberley-Robertson on the abelianizations of certain square complex groups.
We prove that NL is strictly contained in P. We get this separation as a corollary of the following result: the set of context-free languages is not contained in NL. The reader should recall that CFL is contained in DTIME(n^3)
A word is level if each letter appears in it the same number of times, plus or minus 1. We give a complete characterization of the lengths for which level ternary circular square-free words exist. Key words: combinatorics on words, circular…
We determine the basepoint-freeness threshold of a very general polarized abelian surface over the field of complex numbers. We also give the first example of a polarized abelian surface whose basepoint-freeness threshold is irrational.
We prove that the equivariant concordance group $\widetilde{\mathcal{C}}$ is not abelian by exhibiting an infinite family of nontrivial commutators.
The shuffle product \(u\shuffle v\) of two words \(u\) and \(v\) is the set of all words which can be obtained by interleaving \(u\) and \(v\). Motivated by the paper \emph{The Shuffle Product: New Research Directions} by Restivo (2015) we…
Lexical ambiguity presents a profound and enduring challenge to the language sciences. Researchers for decades have grappled with the problem of how language users learn, represent and process words with more than one meaning. Our work…