Search results for "Combinatorics"

Extensions of cocycles for hyperfinite actions and applications

1997

Given a countable, hyperfinite, ergodic and measure-preserving equivalence relationR on a standard probability space (X, ℬ, μ) and an elementW of the normalizerN (R) ofR, we investigate the problem of extendingR-cocycles to\(\bar R\), where\(\bar R\) is the relation generated byR andW. As an application, we obtain that for a Bernoulli automorphism the smallest family of natural factors in sense of [6] consists of all factors. Given an automorphism which is embeddable in a measurable flow and a compact, metric group, we show that for a typical cocycle we cannot lift the whole flow to the centralizer of the corresponding group extension.

On Join Properties of Hall π-Subgroups of Finite π-Soluble Groups

1998

All groups considered in the sequel are finite. K. Doerk and T. Hawkes, in Section I.4 of their recent comprehensive w x volume on finite soluble groups 1 , include background material and a proof of the following result: Let S be a Hall system of a soluble group G and let U and V be subgroups into which S reduces. Then S reduces into U l V, and if , in addition, U permutes with V, then S reduces into UV. It is clear that the second part of the above result holds equally well with a single Hall subgroup in place of a Hall system; in other words, if a Hall p-subgroup of G contains Hall p-subgroups of U and V and U permutes with V, then it also contains a Hall p-subgroup of UV.

Hausdorff measures and dimension

1995

Factored arrangements of hyperplanes

1994

Hölder inequality for functions that are integrable with respect to bilinear maps

2008

Let $(\Omega, \Sigma, \mu)$ be a finite measure space, $1\le p<\infty$, $X$ be a Banach space $X$ and $B:X\times Y \to Z$ be a bounded bilinear map. We say that an $X$-valued function $f$ is $p$-integrable with respect to $B$ whenever $\sup_{\|y\|=1} \int_\Omega \|B(f(w),y)\|^p\,d\mu<\infty$. We get an analogue to Hölder's inequality in this setting.

Unions of identifiable classes of total recursive functions

1992

J.Barzdin [Bar74] has proved that there are classes of total recursive functions which are EX-identifiable but their union is not. We prove that there are no 3 classes U1, U2, U3 such that U1∪U2,U1∪U3 and U2∪U3 would be in EX but U1∪U2∪U3∉ EX. For FIN-identification there are 3 classes with the above-mentioned property and there are no 4 classes U1, U2, U3, U4 such that all 4 unions of triples of these classes would be identifiable but the union of all 4 classes would not. For identification with no more than p minchanges a (2p+2−1)-tuple of such classes do exist but there is no (2p+2)-tuple with the above-mentioned properly.

Characterization of chain geometries of finite dimension by their automorphism group

1990

A large class of chain geometries of finite dimension is characterized as strong chain spaces possessing a distinguished group of automorphisms fixing two distant points.

Divisible Designs Admitting, as an Automorphism Group, an Orthogonal Group or a Unitary Group

2001

We construct some divisible designs starting from a projective space. These divisible designs admit an orthogonal group or a unitary group as an automorphism group.

Injective Fitting sets in automorphism groups

1993

The Ptolemy and Zbăganu constants of normed spaces

2010

Abstract In every inner product space H the Ptolemy inequality holds: the product of the diagonals of a quadrilateral is less than or equal to the sum of the products of the opposite sides. In other words, ‖ x − y ‖ ‖ z − w ‖ ≤ ‖ x − z ‖ ‖ y − w ‖ + ‖ z − y ‖ ‖ x − w ‖ for any points w , x , y , z in H . It is known that for each normed space ( X , ‖ ⋅ ‖ ) , there exists a constant C such that for any w , x , y , z ∈ X , we have ‖ x − y ‖ ‖ z − w ‖ ≤ C ( ‖ x − z ‖ ‖ y − w ‖ + ‖ z − y ‖ ‖ x − w ‖ ) . The smallest such C is called the Ptolemy constant of X and is denoted by C P ( X ) . We study the relationships between this constant and the geometry of the space X , and hence with metric fix…