Covering graphs of various types of finite partially ordered sets have been extensively studied since Ore in [2] asked for a characterization of such graphs in general. In this note we introduce a graph, called the m-chain graph of a poset, that reduces to the covering graph when m = 1. Since we will show how to construct the m-chain graph for m > 2 as the 2-chain graph of another poset, we are...

̂ M of the connection ∇M to the universal cover ̂ M of M is a locally flat connection. The affine structure of ̂ M is defined by a local diffeomorphism DM : ̂ M → R called the developing map. The developing map gives rise to a representation hM : π1 M → Aff R called the holonomy. The linear part L hM of hM is the linear holonomy. The affine manifold M,∇M is complete if and only if DM is a diffeomor...

In this paper, we address a particular variation of the Turán problem for the hypercube. Alon, Krech and Szabó (2007) asked “In an n-dimensional hypercube, Qn, and for ` < d < n, what is the size of a smallest set, S, of Q`’s so that every Qd contains at least one member of S?” Likewise, they asked a similar Ramsey type question: “What is the largest number of colors that we can use to color th...

We describe a general framework for covering concepts using terminologies and briefly present the already investigated instances of this framework. Then, we formalize the best covering problem in the context of the ALN language, in which the difference operation is not semantically unique, and sketches the technique to solve the underlying computation problems.

In the paper we prove a factorization theorem for representations of fundamental groups of compact Kähler manifolds (Kähler groups) into solvable matrix groups. We apply this result to prove that the universal covering of a compact Kähler manifold with a residually solvable fundamental group is holomorphically convex.

in this paper, we develop a capacitated location-covering model considering interval values for demand and service parameters. we also consider flexibility on distance standard for covering demand nodes by the servers. we use the satisfaction degree to represent the constraint of service capacity. the proposed model belongs to the class of mixed integer programming models. our model can be redu...

We point out that there are compact 4-manifolds which do not admit metrics of positive scalar curvature, but nonetheless have finite covering spaces which do carry such metrics. Moreover, passing from a 4-manifold to a covering space sometimes actually changes the sign of the Yamabe invariant. As was first pointed out by Bérard Bergery [1], there exist, in dimensions ≡ 1 or 2 mod 8, n ≥ 9, cert...