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We discuss a homological method for transferring algebra structures on complexes along suitably nice homotopy equivalences, including those obtained after an application of the Perturbation Lemma. We study the implications for the Homotopy…
Let $p$ be an odd prime and $R$ a $p$-torsion-free commutative $\mathbb{Z}_{(p)}$-algebra. We compute the periodic cyclic homology over $R$ of the universal differential graded algebra $R//p$ which is obtained from $R$ by universally…
We present a distributed algorithm to compute the first homology of a simplicial complex. Such algorithms are very useful in topological analysis of sensor networks, such as its coverage properties. We employ spanning trees to compute a…
We propose an algorithm for quickly evaluating polynomials. It pre-conditions a complex polynomial $P$ of degree $d$ in time $O(d\log d)$, with a low multiplicative constant independent of the precision. Subsequent evaluations of $P$…
Cycle sets are algebraic structures introduced by Rump to study set theoretic solutions to the Yang-Baxter equation. While studying cycle sets Rump also introduced braces, which have since overtaken cycle sets as a tool for studying…
We study the Hamilton cycle problem with input a random graph G=G(n,p) in two settings. In the first one, G is given to us in the form of randomly ordered adjacency lists while in the second one we are given the adjacency matrix of G. In…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
The simple connected graphs may be classified by their cycle composition (number and lengths of cycles). This work derives the counting series of the simple connected graphs that have cycles of unrestricted number and length, but no…
This paper presents a query evaluation technique for positive relational algebra queries with aggregates on a representation system for probabilistic data based on the algebraic structures of semiring and semimodule. The core of our…
Assuming sufficiently many terms of a n-dimensional table defined over a field are given, we aim at guessing the linear recurrence relations with either constant or polynomial coefficients they satisfy. In many applications, the table terms…
This paper describes the $K$-theory structure for three algebra classes. For cyclic $p$-group rings and truncated polynomial rings over $\mathbb{Z}/p^s\mathbb{Z}$, we determine reduced $K_2$-structures via a common algebraic framework. For…
In this paper, we consider relational structures arising from Comer's finite field construction, where the cosets need not be sum free. These Comer schemes generalize the notion of a Ramsey scheme and may be of independent interest. As an…
We introduce a new approach that allows us to determine the structure of Zhu's algebra for certain vertex operator (super)algebras which admit horizontal $\mathbb{Z} $-grading. By using this method and an earlier description of Zhu's…
In general terms, we establish algebraic relations that numbers must satisfy in order for their images to match after one or several transformations. Some groups associated with these relationships are identified, such as the Klein group.…
Order-sorted algebras and many sorted algebras exist in a long history with many different implementations and applications. A lot of language specifications have been defined in order-sorted algebra frameworks such as the language…
In this note we provide an algorithm for translating relational structures into "proper" relational structures, i.e., those such that there is no pair of worlds w and u such that w is accessible from u for every agent. In particular, our…
We begin by defining Temperley-Lieb algebra, in two different ways: as a presented algebra or as a diagrammatic algebra. Next, we look for a basis algorithmically, using rewriting theory. Finally, we introduce a generalization of the…
In this paper we show that the $\mathbb Z/p^{m}\mathbb Z$-module structure of the ring $E_p^{(m)}$ is isomorphic to a $\mathbb Z/p^{m}\mathbb Z$-submodule of the matrix ring over $\mathbb Z/p^{m}\mathbb Z$. Using this intrinsic structure of…
This paper studies the complexity of query evaluation for databases whose relations are partially ordered; the problem commonly arises when combining or transforming ordered data from multiple sources. We focus on queries in a useful…