Related papers: Patterns on the numerical duplication by their adm…
We study the algorithmic complexity of embeddings between bi-embeddable equivalence structures. We define the notions of computable bi-embeddable categoricity, (relative) $\Delta^0_\alpha$ bi-embeddable categoricity, and degrees of…
We study a numerical semigroup ring as an algebra over another numerical semigroup ring. The complete intersection property of numerical semigroup algebras is investigated using factorizations of monomials into minimal ones. The goal is to…
In this paper we introduce and study the notion of a graded nil-good ring which is graded by a group. We investigate extensions of graded nil-good rings to graded group rings, Further, we discuss graded matrix ring extensions and trivial…
We introduce and investigate a family of consequence relations with the goal of capturing certain important patterns of data-driven inference. The inspiring idea for our framework is the fact that data may reject, possibly to some degree,…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
We introduce a new Hopf algebra that operates on pairs of finite interval partitions and permutations of equal length. This algebra captures vincular patterns, which involve specifying both the permutation patterns and the consecutive…
Arrangement theory plays an essential role in the study of the unfolding model used in many fields. This paper describes how arrangement theory can be usefully employed in solving the problems of counting (i) the number of admissible…
Grammatical inference is a classical problem in computational learning theory and a topic of wider influence in natural language processing. We treat grammars as a model of computation and propose a novel neural approach to induction of…
A commutative semigroup of abstract factorials is defined in the context of the ring of integers. We study such factorials for their own sake, whether they are or are not connected to sets of integers. Given a subset X of the positive…
For a number field $K$, we extend the notion of the ring class field of an order in $K$ [C. Lv and Y. Deng, SciChina. Math., 2015] to that of an arbitrary number ring in $K$. We give both ideal-theoretic and idele-theoretic description of…
A \emph{numerical semigroup} is a subset $\Lambda$ of the nonnegative integers that is closed under addition, contains $0$, and omits only finitely many nonnegative integers (called the \emph{gaps} of $\Lambda$). The collection of all…
Let f be a computable function from finite sequences of 0's and 1's to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also prove: if X is strongly f-random and Turing reducible to Y…
We use homotopy theory to define certain rational coefficients characteristic numbers with integral values, depending on a given prime number q and positive integer t. We prove the first nontrivial degree formula and use it to show that…
This paper studies the class group of graded integral domains. As an application, we state a decomposition theorem for class groups of semigroup rings. This recovers well-known results developed for the classic contexts of polynomial rings…
Frieze patterns are numerical arrangements that satisfy a local arithmetic rule. These arrangements are actively studied in connection to the theory of cluster algebras. In the setting of cluster algebras, the notion of a frieze pattern can…
We introduce graded $\mathbb{E}_{\infty}$-rings and graded modules over them, and study their properties. We construct projective schemes associated to connective $\mathbb{N}$-graded $\mathbb{E}_{\infty}$-rings in spectral algebraic…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
The use of patterns in predictive models is a topic that has received a lot of attention in recent years. Pattern mining can help to obtain models for structured domains, such as graphs and sequences, and has been proposed as a means to…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…