Related papers: A Taxonomy of Morphic Sequences
Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.
We consider a notion of exact sequences in any -not necessarily exact- pointed category relative to a given (E;M)-factorization structure. We apply this notion to introduce and investigate a new notion of exact sequences of semimodules over…
An infinite binary sequence is deemed to be random if it has all definable properties that hold almost surely for the usual probability measure on the set of infinite binary sequences. There are only countably many such properties, so it…
We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and…
Given an abelian category, we characterize the long exact sequences of length six which can be obtained from the snake lemma. Equivalently, these are the long exact sequences which arise as the homology of a triangle in the corresponding…
We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula…
We rewrite classical topological definitions using the category-theoretic notation of arrows and are led to concise reformulations in terms of simplicial categories and orthogonality of morphisms, which we hope might be of use in the…
In this paper, we characterize the monoid of endomorphisms of the semigroup of all monotone full transformations of a finite chain, as well as the monoids of endomorphisms of the semigroup of all monotone partial transformations and of the…
A decomposition of a natural number n is a sequence of consecutive natural numbers that sums to n. We construct a one-to-one correspondence between the odd factors of a natural number and its decompositions. We study the decompositions by…
In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.
We introduce a categorical analogue of Saito's notion of primitive forms. Let $W$ denote the potential $\frac{1}{n+1} x^{n+1}$. For the category $MF(W)$ of matrix factorizations of $W$ we prove that there exists a unique, up to non-zero…
Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns…
A separable, proper morphism of varieties with geometrically connected fibers induces a homotopy exact sequence relating the \'etale fundamental groups of source, target and fiber. Extending work of dos Santos, we prove the existence of an…
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
Let $ \prod_{i=1}^d (X-\alpha_i Y) \in{\mathbb C}[X,Y]$ be a binary form and let $\epsilon_1,\dots,\epsilon_d$ be nonzero complex numbers. We consider the family of binary forms $ \prod_{i=1}^d (X-\alpha_i \epsilon_i^aY)$, $a\in {\mathbb…
Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…
This paper describes new, simple, recursive methods of construction for orientable sequences, i.e. periodic binary sequences in which any n-tuple occurs at most once in a period in either direction. As has been previously described, such…
The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…
Finding integer solutions to norm form equations is a classical Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It is known that these solutions can be…
We classify all of the groups with twelve or fewer subgroups. This paper is the proof of the entries in a submission to the Online Encyclopedia of Integer Sequences.