In a recent paper by this author, constructions of linear binary covering codes are considered. In this work, constructions and techniques of the earlier paper are developed and modified for q-ary linear nonbinary covering codes, q 2 3, and new constructions are proposed. The described constructions design an infinite family of codes with covering radius R based on a starting code of the same c...

We show that if a knot exterior satis"es certain conditions, then it has "nite cyclic coverings with arbitrarily large numbers of nontrivial algebraic components in their SL(2, ) character varieties (Theorem A). As an example, these conditions hold for hyperbolic punctured torus bundles over the circle (Theorem B). We investigate in more detail the "nite cyclic covers of the "gure-eight knot ex...

In this paper we analyse the complexity of boolean functions takes value 0 on a sufficiently small number of points. For many functions this leads to the analysis of a single function attains 0 only on unsigned representation of numbers from 1 to d for various d. Here we obtain a tight bounds on the DNF complexity of complete functions in terms of the number of literals and conjunctions. The me...

We write down the chain complex C∗ of the universal cover of the torus, and indicate how to do likewise for any 2-dimensional CW complex arising as the 2-skeleton of a K(G, 1). We exhibit a contracting chain homotopy for this chain complex, and again explain how to do so for the chain complex of the universal cover of our more general CW complex. This yields a contracting homotopy for the tenso...

let $gamma(s_n)$ be the minimum number of proper subgroups‎ ‎$h_i, i=1‎, ‎dots‎, ‎l $ of the symmetric group $s_n$ such that each element in $s_n$‎ ‎lies in some conjugate of one of the $h_i.$ in this paper we‎ ‎conjecture that $$gamma(s_n)=frac{n}{2}left(1-frac{1}{p_1}right)‎ ‎left(1-frac{1}{p_2}right)+2,$$ where $p_1,p_2$ are the two smallest primes‎ ‎in the factorization of $ninmathbb{n}$ an...

In this note, we prove the generic Kobayashi volume measure hyperbolicity of singular directed varieties (X,V ), as soon as the canonical sheaf KV of V is big in the sense of Demailly.

In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of covering-based rough sets and some existing special matroids. Firstly, as an extension of partitions, coverings are more natural combinatorial objects and can sometimes be more efficient to deal with problems in the real world. Through extending partitions to cover...

We develop an explicit covering theory for complexes of groups, parallel to that developed for graphs of groups by Bass. Given a covering of developable complexes of groups, we construct the induced monomorphism of fundamental groups and isometry of universal covers. We characterize faithful complexes of groups and prove a conjugacy theorem for groups acting freely on polyhedral complexes. We a...

We study the existence of geometrically controlled branched covering maps from R to open 3-manifolds or to decomposition spaces S/G, and from S/G to S. Dedicated to the memory of Fred Gehring, whose work has been our inspiration

In this paper we define, for each aspherical orientable 3-manifold M endowed with a torus splitting T , a 2-dimensional fundamental l1-class [M ] whose l1norm has similar properties as the Gromov simplicial volume of M (additivity under torus splittings and isometry under finite covering maps). Next, we use the Gromov simplicial volume of M and the l1-norm of [M ] to give a complete characteriz...