Related papers: The infinitary n-cube shuffle

In two previous papers we constructed new families of completely regular codes by concatenation methods. Here we determine cases in which the new codes are completely transitive. For these cases we also find the automorphism groups of such…

We proved in a previous article that the bar complex of an E-infinity algebra inherits a natural E-infinity algebra structure. As a consequence, a well-defined iterated bar construction B^n(A) can be associated to any algebra over an…

We show that the automorphism group of every zero entropy infinite shift admits a "drift" homomorphism to $(\mathbb{R},+)$ that maps the shift map to 1. This homomorphism arises as the expectation, under an invariant measure, of a cocycle…

An $n$-dimensional rep-tile is a compact, connected submanifold of $\mathbb{R}^n$ with non-empty interior which can be decomposed into pairwise isometric rescaled copies of itself whose interiors are disjoint. We show that every smooth…

We show that for non-conjugate subgroups $G_1$ and $G_2$ of a finite group $G$ there exists an extension of $G$ (by a finite group) in which the pre-images of $G_1$ and $G_2$ are not isomorphic. This allows us to show that $\mathbb Z$-coset…

After 1-point compactification, the collection of all unordered configuration spaces of a manifold admits a commutative multiplication by superposition of configurations. We explain a simple (derived) presentation for this commutative…

This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…

We exhibit a simple condition under which a finite involutary semigroup whose semigroup reduct is inherently nonfinitely based is also inherently nonfinitely based as a unary semigroup. As applications, we get already known as well as new…

In this article, we will prove a full topological version of Popa's measurable cocycle superrigidity theorem for full shifts. More precisely, we prove that every H\"older continuous cocycle for the full shifts of every finitely generated…

Relying on the computation of the Andre-Quillen homology groups for unstable Hopf algebras, we prove that the mod p cohomology of the n-connected cover of a finite H-space is always finitely generated as algebra over the Steenrod algebra.

The moduli spaces of theta-semistable representations of a finite quiver can be packaged together to form a noncommutative compact manifold.

The well-known Eckmann-Hilton Principle may be applied to prove that fundamental groups of $H$-spaces are commutative. In this paper, we identify an infinitary analogue of the Eckmann-Hilton Principle that applies to fundamental groups of…

For a $p$-permutation equivalence between two block algebras of finite groups, we introduce new square diagrams that link the $p$-permutation equivalence via the Brauer construction to local equivalences between stabilizers of corresponding…

We construct unital extensions of the higher order peak algebras defined by Krob and the third author in [Ann. Comb. 9 (2005), 411--430.], and show that they can be obtained as homomorphic images of certain subalgebras of the…

A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…

We define a notion of (one-sided) edge shift spaces associated to ultragraphs. In the finite case our notion coincides with the edge shift space of a graph. In general, we show that our space is metrizable and has a countable basis of…

The sets of primitive, quasiprimitive, and innately transitive permutation groups may each be regarded as the building blocks of finite transitive permutation groups, and are analogues of composition factors for abstract finite groups. This…

For $X$ a connected finite simplicial complex we consider $\Delta^d(X,n)$ the space of configurations of $n$ ordered points of $X$ such that no $d+1$ of them are equal, and $B^d(X,n)$ the analogous space of configurations of unordered…

We present a new approach to simple homotopy theory of polyhedra using finite topological spaces. We define the concept of collapse of a finite space and prove that this new notion corresponds exactly to the concept of a simplicial…

We show that if a complex has free finitely generated reduced homology groups for two consecutive dimensions and trivial homology for all other dimensions, then it must have the homotopy type of a wedge of spheres of two consecutive…