Related papers: The non-abelian squares are not context-free
We investigate Abelian primitive words, which are words that are not Abelian powers. We show that unlike classical primitive words, the set of Abelian primitive words is not context-free. We can determine whether a word is Abelian primitive…
The paper demonstrates the non-closure of the family of unambiguous linear languages (that is, those defined by unambiguous linear context-free grammars) under complementation. To be precise, a particular unambiguous linear grammar is…
We consider the class of groups whose word problem is poly-context-free; that is, an intersection of finitely many context-free languages. We show that any group which is virtually a finitely generated subgroup of a direct product of free…
We show that the set of binary words containing overlaps is not unambiguously context-free and that the set of ternary words containing overlaps is not context-free. We also show that the set of binary words that are not subwords of the…
We present and discuss a number of known results and open problems abelian squares in words on small alphabets.
We provide the first examples of words in the free group of rank 2 which are not proper powers and for which the corresponding word maps are non-surjective on an infinite family of finite non-abelian simple groups.
We show that the number of length-n words over a k-letter alphabet having no even palindromic prefix is the same as the number of length-n unbordered words, by constructing an explicit bijection between the two sets. A slightly different…
A word is square-free if it does not contain any square (a word of the form $XX$), and is extremal square-free if it cannot be extended to a new square-free word by inserting a single letter at any position. Grytczuk, Kordulewski, and…
In this paper we give an example of a linear group such that its tensor square is not linear. Also, we formulate some sufficient conditions for the linearity of non-abelian tensor products $G \otimes H$ and tensor squares $G \otimes G$.…
We study the structure of the language of binary cube-free words. Namely, we are interested in the cube-free words that cannot be infinitely extended preserving cube-freeness. We show the existence of such words with arbitrarily long finite…
It was recently proven that all free and many virtually free verbally closed subgroups are algebraically closed in any group. We establish sufficient conditions for a group that is an extension of a free non-abelian group by a group…
We give in this paper a logical characterization for unambiguous Context Free Languages, in the vein of descriptive complexity. A fragment of the logic characterizing context free languages given by Lautemann, Schwentick and Th\'erien [18]…
We prove that episturmian words and Arnoux-Rauzy sequences can be characterized using a local balance property. We also give a new characterization of epistandard words and show that the set of finite words that are not factors of an…
We prove that there exists no algorithm to decide whether the language generated by a context-free grammar is dense with respect to the lexicographic ordering. As a corollary to this result, we show that it is undecidable whether the…
An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain $\Theta(n^2)$ distinct factors that are abelian squares. We study infinite words such that the number of abelian square…
We study the full language of quasigeodesics in Cayley graphs, with fixed error constants. We show that, given a non-virtually-cyclic nilpotent group or Baumslag--Solitar group, and any finite generating set, such languages fail to be…
We give examples of smooth $\k$-unirational line-free quartic hypersurfaces over a non algebraically closed field $\k$. Unlike other methods of proving unirationality, our method does not rely on existence of linear spaces on quartics.
We prove that the abstract commensurator of a nonabelian free group, an infinite surface group, or more generally of a group that splits appropriately over a cyclic subgroup, is not finitely generated. This applies in particular to all…
We discuss the conditions under which non-abelian T-duality can be considered as a chain of abelian T-dualities. Motivated by these results, we propose that the topology of a non-abelian T-dual should be phrased in the language of T-folds,…
In this paper, we prove the semidecidability of the problem of saying whether or not a context-free grammar generates a regular language. We introduce the notion of context-free grammar in Marciani Normal Form. We prove that a context-free…