2003http://hdl.handle.net/123456789/252019-08-22T05:05:41Z2019-08-22T05:05:41ZOn faithful actions of groups and semigroups by orientation-preserving plane isometriesVorobets, Yaroslavhttp://hdl.handle.net/123456789/822015-10-27T16:56:03Z2003-01-01T00:00:00ZOn faithful actions of groups and semigroups by orientation-preserving plane isometries
Vorobets, Yaroslav
Feitful representations of two generated free
groups and free semigroups by orientation-preserving plane isometries
constructed.
2003-01-01T00:00:00ZStructural properties of extremal asymmetric coloringsVerbitsky, Oleghttp://hdl.handle.net/123456789/812015-10-27T16:54:49Z2003-01-01T00:00:00ZStructural properties of extremal asymmetric colorings
Verbitsky, Oleg
Let be a space with probability measure μ
for which the notion of symmetry is defined. Given A µ , let
ms(A) denote the supremum of μ(B) over symmetric B µ A. An
r-coloring of is a measurable map Â : ! {1, . . . , r} possi-
bly undefined on a set of measure 0. Given an r-coloring Â, let
ms(; Â) = max1·i·r ms(Â−1(i)). With each space we associate
a Ramsey type number ms(, r) = infÂms(; Â). We call a col-
oring Â congruent if the monochromatic classes Â−1(1), . . . , Â−1(r)
are pairwise congruent, i.e., can be mapped onto each other by a
symmetry of . We define ms?(, r) to be the infimum of ms(; Â)
over congruent Â.
We prove that ms(S1, r) = ms?(S1, r) for the unitary circle S1
endowed with standard symmetries of a plane, estimate ms?([0, 1), r)
for the unitary interval of reals considered with central symmetry,
and explore some other regularity properties of extremal colorings
for various spaces.
2003-01-01T00:00:00ZDynamics of finite groups acting on the boundary of homogenous rooted treeSzaszkowski, Zbigniewhttp://hdl.handle.net/123456789/802015-10-27T16:56:57Z2003-01-01T00:00:00ZDynamics of finite groups acting on the boundary of homogenous rooted tree
Szaszkowski, Zbigniew
Criterion of embedding of finite groups into the
automorphism groups of a homogenous rooted tree of a spherical
index n is formulated. The sets of natural numbers which are the
lengths of all orbits of finite groups acting on the boundary of tree
are described.
2003-01-01T00:00:00ZOn 2-state Mealy automata of polynomial growthReznykov, I. I.http://hdl.handle.net/123456789/792015-10-27T16:56:30Z2003-01-01T00:00:00ZOn 2-state Mealy automata of polynomial growth
Reznykov, I. I.
We consider the sequence of 2-state Mealy au-
tomata over the finite alphabets, that have polynomial growth or-
ders and define the infinitely presented automatic transformation
semigroups.
2003-01-01T00:00:00Z