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Palindromic width of wreath products, metabelian groups, and max-n solvable groups
wreath products metabelian groups
2015/8/26
A group has finite palindromic width if there exists n such that every element can be expressed as a product of n or fewer palindromic words. We show that if G has finite palindromic width with respec...
Guaranteed Conservative Fixed Width Confidence Intervals Via Monte Carlo Sampling
Intervals Via Monte Carlo Sampling Guaranteed Conservative
2015/8/21
Monte Carlo methods are used to approximate the means, μ, of random variables
Y, whose distributions are not known explicitly. The key idea is that the average of a random
sample, Y1,...,Yn, tends t...
Abstract: We prove that, for each nonnegative integer k and each matroid N, if M is a 3-connected matroid containing N as a minor, and the the branch width of M is sufficiently large, then there is a ...
Verbal subgroups of hyperbolic groups have infinite width
Verbal subgroups hyperbolic groups Group Theory
2011/9/14
Abstract: Let $G$ be a non-elementary hyperbolic group. Let $w$ be a group word such that the set $w[G]$ of all its values in $G$ does not coincide with $G$ or 1. We show that the width of verbal subg...
Pole solutions in formation of the Saffman-Teylor "finger" with one half of the channel width without surface tension
surface tension integro-differential motion equations Laplacian growth
2011/7/5
Laplacian growth without surface tension has nice analytical solutions which replace its complex integro-differential motion equations by simple differential equations of poles motion in a complex pla...
Group Width
Group Width Geometric Topology
2010/11/18
There are many "minimax" complexity functions in mathematics: width of a tree or a link, Heegaard genus of a 3-manifold, the Cheeger constant of a Riemannian manifold. We define such a function w, "wi...
Sub-Gaussian tail bounds for the width and height of conditioned Galton--Watson trees
Sub-Gaussian tail conditioned Galton--Watson trees
2010/11/23
We study the height and width of a Galton--Watson tree with offspring distribution B satisfying E(B)=1, 0 < Var(B) < infinity, conditioned on having exactly n nodes. Under this conditioning, we deriv...
Vertex subsets with minimal width and dual width in $Q$-polynomial distance-regular graphs
Vertex subsets $Q$-polynomial distance-regular graphs
2010/11/15
We study $Q$-polynomial distance-regular graphs from the point of view of what we call descendents, that is to say, those vertex subsets with the property that the width $w$ and dual width $w^*$ sati...
Analysis of Width-$w$ Non-Adjacent Forms to Imaginary Quadratic Bases
-adic expansions non-adjacent forms redundant digit sets
2010/11/29
We consider digital expansions to the base of , where is an algebraic integer. For a w 2, the set of admissible digits consists of 0 and one representative of every residue class modulo w which ...
Local tree-width, excluded minors, and approximation algorithms
Local tree-width excluded minors approximation algorithms
2010/11/1
The local tree-width of a graph G=(V,E) is the function ltw^G: N -> N that associates with every natural number r the maximal tree-width of an r-neighborhood in G. Our main graph theoretic result is ...