Random coverings
نویسندگان
چکیده
منابع مشابه
Properties of random coverings of graphs
In the thesis we study selected properties of random coverings of graphs introduced by Amit and Linial in 2002. A random n-covering of a graph G, denoted by G̃, is obtained by replacing each vertex v of G by an n-element set G̃v and then choosing, independently for every edge e = {x, y} ∈ E(G), uniformly at random a perfect matching between G̃x and G̃y. The first problem we consider is the typical ...
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In this paper we describe a simple model for random graphs that have an n-fold covering map onto a fixed finite base graph. Roughly, given a base graph G and an integer n, we form a random graph by replacing each vertex of G by a set of n vertices, and joining these sets by random matchings whenever the corresponding vertices are adjacent in G. The resulting graph covers the original graph in t...
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Fuchsian groups (acting as isometries of the hyperbolic plane) occur naturally in geometry, combinatorial group theory, and other contexts. We use character-theoretic and probabilistic methods to study the spaces of homomorphisms from Fuchsian groups to symmetric groups. We obtain a wide variety of applications, ranging from counting branched coverings of Riemann surfaces, to subgroup growth an...
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A rectifier network is a directed acyclic graph with distinguished sources and sinks; it is said to compute a Boolean matrix M that has a 1 in the entry (i, j) iff there is a path from the jth source to the ith sink. The smallest number of edges in a rectifier network that computes M is a classic complexity measure on matrices, which has been studied for more than half a century. We explore two...
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 1977
ISSN: 0001-5962
DOI: 10.1007/bf02392317