Related papers: On The Structure of Dyck Languages
In this paper we study double cosets of finite rank free groups. We focus our attention on cancellation types in double cosets and their formal language properties.
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 a certain linear representation of the singular braid monoid on three strands is faithful. Furthermore we will give a second - group theoretically motivated - solution to the word problem in this monoid.
A monoid $S$ is said to be right coherent if every finitely generated subact of every finitely presented right $S$-act is finitely presented. Left coherency is defined dually and $S$ is coherent if it is both right and left coherent. These…
We prove that monoids $\mathrm{Mon}\langle a,b,c,d : a^nb=0, ac=1, db=1, dc=1, dab=1, da^2b=1, \ldots, da^{n-1}b=1\rangle$ are congruence-free for all $n\geq 1$. This provides a new countable family of finitely presented congruence-free…
q-rook monoid algebras, Hecke algebras and Schur-Weyl duality
Using a construction that builds a monoid from a monoid action, this paper exhibits an example of a direct product of monoids that admits a prefix-closed regular cross-section, but one of whose factors does not admit a regular…
We describe a simple scheme for constructing finitely generated monoids in which left-divisibility is a linear ordering and for practically investigating these monoids. The approach is based on subword reversing, a general method of…
Many formalisms combining ontology languages with uncertainty, usually in the form of probabilities, have been studied over the years. Most of these formalisms, however, assume that the probabilistic structure of the knowledge remains…
We give a new proof of Salvati's theorem that the group language $O_2$ is $2$ multiple context free. Unlike Salvati's proof, our arguments do not use any idea specific to two-dimensions. This raises the possibility that the argument might…
We initiate the study of expansions of monoids in the class of two-sided restriction monoids and show that generalizations of the Birget-Rhodes prefix group expansion, despite the absence of involution, have rich structure close to that of…
A free resolution of free partially commutative monoids is constructed and with its help the homological dimension of these monoids is calculated.
We construct a compact closed category out of any symmetric monoidal category by freely adding adjoints to its objects. The morphisms of the completion are defined as string diagrams annotated by objects and morphisms from the original…
We prove that the Parikh map of a bounded context-free language is a box spline. Moreover we prove that in this case, such a function is rational.
We show that some results from the theory of group automata and monoid automata still hold for more general classes of monoids and models. Extending previous work for finite automata over commutative groups, we demonstrate a context-free…
We give a proof of the fact tha the subset of the rational curves form a closed analytic subset in the space of the 1-dimensional cycles of a complex space.
We show that a transverse link in a contact structure supported by an open book decomposition can be transversely braided. We also generalize Markov's theorem on when the closures of two braids represent (transversely) isotopic links.
The network characteristics based on the phonological similarities in the lexicons of several languages were examined. These languages differed widely in their history and linguistic structure, but commonalities in the network…
We consider two-variable first-order logic on finite words with a fixed number of quantifier alternations. We show that all languages with a neutral letter definable using the order and finite-degree predicates are also definable with the…
A monoid presentation is called special if the right-hand side of each defining relation is equal to 1. We prove results which relate the two-sided homological finiteness properties of a monoid defined by a special presentation with those…