Related papers: Constructing balleans
Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.
In this paper, six constructions of difference families are presented. These constructions make use of difference sets, almost difference sets and disjoint difference families, and give new point of views of relationships among these…
Scaled Boolean algebras are a category of mathematical objects that arose from attempts to understand why the conventional rules of probability should hold when probabilities are construed, not as frequencies or proportions or the like, but…
We construct 3-manifolds which have at least two inequivalent embeddings such that both complementary regions have abelian fundamental group.
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…
A subset $A$ of a commutative semigroup $X$ is called a $B_h$ set in $X$ if the only solutions to $a_1+\dots+a_h = b_1 + \cdots +b_h$ (with $a_i,b_i \in A$) are the trivial solutions $\{a_1,\dots,a_h\} = \{b_1,\dots,b_h\}$ (as multisets).…
The purpose of this paper is to give an effective construction for some induced structures on spheres or product of spheres of codimension 1, 2 or 3, respectively, in Euclidean space endowed with an almost product structure.
We describe and analyze a new construction that produces new Eulerian lattices from old ones. It specializes to a construction that produces new strongly regular cellular spheres (whose face lattices are Eulerian). The construction does not…
This paper discusses the question of how to recognize whether an operad is E_n (ie. equivalent to the little n-cubes operad). A construction is given which produces many new examples of E_n operads. This construction is developed in the…
An algebraic structure with two constants and one ternary operation, which is not completely commutative, is put forward to accommodate ternary Boolean algebras. When the ternary operation is interpreted as Church's conditioned disjunction,…
Bars have a complex three-dimensional shape. In particular their inner part is vertically much thicker than the parts further out. Viewed edge-on, the thick part of the bar is what is commonly known as a boxy-, peanut- or X- bulge and…
When a solenoid is embedded in three space, its complement is an open three manifold. We discuss the geometry and fundamental groups of such manifolds, and show that the complements of different solenoids (arising from different inverse…
We investigate sigma-entangled linear orders and narrowness of Boolean algebras. We show existence of sigma-entangled linear orders in many cardinals, and we build Boolean algebras with neither large chains nor large pies. We study the…
In this paper, we mainly investigate profound interconnections between combinatorial designs, linear codes, and Boolean functions.
We exhaustively investigate possible combinations of a boolean operation together with a catenation. In many cases we prove and improve some conjectures by Brzozowski. For each family of operation, we endeavour to provide a common witness…
A family of algebraic surfaces with many nondegenerate real singularities is introduced with the help of a construction, which has been used in previous works for the generation of substitution tilings.
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the properties of dual dimonoids. In the class of noncommutative…
A basic family of solenoids is discussed, especially from the point of view of analysis on metric spaces.
We present a bijective algorithm with which an arbitrary permutation decomposes canonically into elementary blocks which we call families, which are sets with a specified number of ascents and descents. We show that families, arranged in an…