Related papers: Rational sets in virtually abelian groups: languag…
Given a Lie algebra $L$ graded by a group $G$, if $L$ is does not contain orthogonal graded ideals and $G$ is generated by the support of $L$, then $G$ is an abelian group.
We study some subsets of rational points in an algebraic groups defined by open conditions on their projection in the finite adeles points. Using adelic mixing we are able to prove an equidistribution's result for the projection of these…
The correspondence between perfect difference sets and transitive projective planes is well-known. We observe that all known dense (i.e., close to square-root size) Sidon subsets of abelian groups come from projective planes through a…
This study investigates how BERT processes and represents Argument Structure Constructions (ASCs), extending previous LSTM analyses. Using a dataset of 2000 sentences across four ASC types (transitive, ditransitive, caused-motion,…
Let $G$ be the fundamental group of a compact nonpositively curved cube complex $Y$. With respect to a basepoint $x$, one obtains an integer-valued length function on $G$ by counting the number of edges in a minimal length edge-path…
A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This paper gives a systematic analysis of the properties…
Let $M(A,I)$ be a free partially commutative monoid with involution and $G(A,I)$ be its quotient group, e.g. a right-angled Artin or Coxeter group. Given a system of word equations over $M(A,I)$ with recognizable constraints with input size…
A commuting family of subnormal operators need not have a commuting normal extension. We study when a representation of an abelian semigroup can be extended to a normal representation, and show that it suffices to extend the set of…
Natural logic offers a powerful relational conception of meaning that is a natural counterpart to distributed semantic representations, which have proven valuable in a wide range of sophisticated language tasks. However, it remains an open…
We give a method for effectively generating generalised loxodromics in subgroups of graph products, using positive words. This has several consequences for the growth of subsets of these groups. In particular, we show that graph products of…
In this paper, we introduce the concept of Denjoy-Wolff set in rational semigroups. We show that for finitely generated Abelian rational semigroups, the Denjoy-Wolff like set is countable. Some results concerning the Denjoy-Wolff like set…
We investigate the algebraic K- and L-theory of the group ring RG, where G is a hyperbolic or virtually finitely generated abelian group and R is an associative ring with unit.
A complex vector space $V$ is an \'etale $G$-module if $G$ acts rationally on $V$ with a Zariski-open orbit and $\dim G=\dim V$. Such a module is called super-\'etale if the stabilizer of a point in the open orbit is trivial. Popov proved…
We prove that the numbers of irreducible n-dimensional complex continuous representations of the special linear groups over p-adic integers grow slower than the square of n. We deduce that the abscissas of convergence of the representation…
We investigate certain word-construction games with variable turn orders. In these games, Alice and Bob take turns on choosing consecutive letters of a word of fixed length, with Alice winning if the result lies in a predetermined target…
We consider Delone sets with finite local complexity. We characterize validity of a subadditive ergodic theorem by uniform positivity of certain weights. The latter can be considered to be an averaged version of linear repetitivity. In this…
Futrell and Mahowald (2025) frame the success of neural language models (LMs) as supporting gradient, usage-based linguistic theories. I argue that LMs can also instantiate theories based on formal structures - the types of theories seen in…
As mathematical induction is applied to prove statements on natural numbers, {\it continuous induction} (or, {\it real induction}) is a tool to prove some statements in real analysis.(Although, this comparison is somehow an overstatement.)…
We introduce an elementary class of linearly ordered groups, called growth order groups, encompassing certain groups under composition of formal series (e.g. transseries) as well as certain groups $\mathcal{G}_{\mathcal{M}}$ of infinitely…
Humans construct internal world models and reason by manipulating the concepts within these models. Recent advances in AI, particularly chain-of-thought (CoT) reasoning, approximate such human cognitive abilities, where world models are…