An inequality for permanent of (0, 1)-matrices

AbstractLet A be an n-square (0, 1)-matrix, let ri denote the i-th row sum of A, i=1, …, n, and let per (A) denote the permanent of A. Then per(A)≤∏i=1nri+21+2 where equality can occur if and only if there exist permutation matrices P and Q such that PAQ is a direct sum of 1-square and 2-square matrices all of whose entries are 1

On simplicial maps and chainable continua

AbstractAn operation d on simplicial maps between graphs is introduced and used to characterize simplicial maps which can be factored through an arc. The characterization yields a new technique of showing that some continua are not chainable and allows to prove that span zero is equivalent to chainability for inverse limits of trees with simplicial bonding maps

Bihomogeneity of solenoids

Solenoids are inverse limit spaces over regular covering maps of closed manifolds. M.C. McCord has shown that solenoids are topologically homogeneous and that they are principal bundles with a profinite structure group. We show that if a solenoid is bihomogeneous, then its structure group contains an open abelian subgroup. This leads to new examples of homogeneous continua that are not bihomogeneous.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-1.abs.htm

Scaling properties of centering forces

Motivated by the centering of biological objects in large cells, we study the generic properties of centering forces inside a ball (or a volume of spherical topology) in $n$ dimensions. We consider two scenarios : autonomous centering (in which distance information is integrated from the agent perspective) and non-autonomous centering (in which distance to the surface is integrated over the whole surface). We find relations between the net centering force and the mean distance$^p$ to the surface. This allows us to find simple scaling laws between the centering force and the distance to the center, as a function of the dimensionality $n$. Interestingly, if the interactions between the agent and the surface are hyper-elastic, the net centering force can still be sub-elastic in the case of autonomous centering. These scaling laws are increasingly violated as the space becomes less convex. Generically, neither scenarios exactly converge to the center of mass of the space