Graph coverings are known to induce surjections of their critical groups. Here we describe the kernels of these morphisms in terms of data parametrizing the covering. Regular coverings are parametrized by voltage graphs, and the above kernel can be identified with a naturally defined voltage graph critical group. For double covers, the voltage graph is a signed graph, and the theory takes a par...

We construct and study two series of curves whose Jacobians admit complex multiplication. The curves arise as quotients of Galois coverings of the projective line with Galois group metacyclic groups Gq,3 of order 3q with q ≡ 1 mod 3 an odd prime, and Gm of order 2 . The complex multiplications arise as quotients of double coset algebras of the Galois groups of these coverings. We work out the C...

This paper addresses the following questions for a given tree T and integer d ≥ 2: (1) What is the minimum number of degree-d subtrees that partition E(T )? (2) What is the minimum number of degree-d subtrees that cover E(T )? We answer the first question by providing an explicit formula for the minimum number of subtrees, and we describe a linear time algorithm that finds the corresponding par...

Some approaches to the covering information entropy and some definitions of orderings and quasi–orderings of coverings will be described, generalizing the case of the partition entropy and ordering. The aim is to extend to covering the general result of anti–tonicity (strictly decreasing monotonicity) of partition entropy. In particular an entropy in the case of incomplete information systems i...

Past studies of the Brauer group of a scheme tells us the importance of the interrelationship among Brauer groups of its finite étale coverings. In this paper, we consider these groups simultaneously, and construct an integrated object “BrauerMackey functor”. We realize this as a cohomological Mackey functor on the Galois category of finite étale coverings. For any finite étale covering of sche...

This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation of fuzzy coverings for fuzzy covering rough sets, the concepts of fuzzy subcoverings, the reducible and intersectional elements, the union and intersection o...

A tolerance is a reflexive and symmetric, but not necessarily transitive, binary relation. Contrary what happens with equivalence relations, when dealing with tolerances one must distinguish between blocks (maximal subsets where the tolerance is a total relation) and classes (the class of an element is the set of those elements tolerable with it). Both blocks and classes of a tolerance on a set...

Abstract. In this paper, n-fold branched coverings of a closed nonorientable surface S of genus p with r ≥ 1 cyclic branch points (that is, such that all ramification points over them are of multiplicity n) are considered. The number Np, r(n) of such coverings up to equivalence is evaluated explicitly in a closed form (without using any complicated functions such as irreducible characters of th...