Related papers: Simple Classes of Automatic Structures
We define the operation of composing two hereditary classes of permutations using the standard composition of permutations as functions and we explore properties and structure of permutation classes considering this operation. We mostly…
We introduce graphical complexes of groups, which can be thought of as a generalisation of Coxeter systems with 1-dimensional nerves. We show that these complexes are strictly developable, and we equip the resulting Basic Construction with…
We classify non symplectic prime order automorphisms and all finite order symplectic automorphism groups of generalised Kummer fourfolds using lattice theory and recent results on ample cones and monodromy groups. We study various geometric…
This article discuss a class of tractable model in the form of polynomial type.
We classify a class of infinite-dimensional simple graded pre-Lie algebras on the graded vector space underlying the algebra of Laurent polynomials, with a specific form for the product.
We study the representation theory of three towers of algebras which are related to the symmetric groups and their Hecke algebras. The first one is constructed as the algebras generated simultaneously by the elementary transpositions and…
We study natural linear representations of self-similar groups over finite fields. In particular, we show that if the group is generated by a finite automaton, then obtained matrices are automatic. This shows a new relation between two…
Parikh automata extend automata with counters whose values can only be tested at the end of the computation, with respect to membership into a semi-linear set. Parikh automata have found several applications, for instance in transducer…
We develop a novel combinatorial perspective on the higher Auslander algebras of type $\mathbb{A}$, a family of algebras arising in the context of Iyama's higher Auslander-Reiten theory. This approach reveals interesting simplicial…
We describe an incremental algorithm to enumerate the isomorphism classes of double pseudoline arrangements. The correction of our algorithm is based on the connectedness under mutations of the spaces of one-extensions of double pseudoline…
This paper presents new results from a detailed study of the structure of autocatalytic sets. We show how autocatalytic sets can be decomposed into smaller autocatalytic subsets, and how these subsets can be identified and classified. We…
We show how the framework of crossed simplicial groups may be used to provide a classification of topological field theories on open cobordism categories defined by reductions of the structure group to a planar Lie group. Such theories are…
Automata admitting at most one accepting run per structure, known as unambiguous automata, find applications in verification of reactive systems as they extend the class of deterministic automata whilst maintaining some of their desirable…
Over the last 20 years a large number of automata-based specification theories have been proposed for modeling of discrete,real-time and probabilistic systems. We have observed a lot of shared algebraic structure between these formalisms.…
One of the four well-known series of simple Lie algebras of Cartan type is the series of Lie algebras of Special type, which are divergence-free Lie algebras associated with polynomial algebras and the operators of taking partial…
We study subsystems of open induction which are strongly connected to methods of automated inductive theorem proving. Specifically, we consider systems obtained from restricting induction to atoms, literals, clauses, and dual clauses. We…
The structure of the automorphism group of the sandwich semigroup IS_n is described in terms of standard group constructions.
Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…
Two supersymmetric classical mechanical systems are discussed. Concrete realizations are obtained by supposing that the dynamical variables take values in a Grassmann algebra with two generators. The equations of motion are explicitly…
We introduce some new symmetric tensor categories based on the combinatorics of trees: a discrete family $\mathcal{D}(n)$, for $n \ge 3$ an integer, and a continuous family $\mathcal{C}(t)$, for $t \ne 1$ a complex number. The construction…