Related papers: Measures for the colored circle
In the present paper, we show that many combinatorial and topological objects, such as maps, hypermaps, three-dimensional pavings, constellations and branched coverings of the two--sphere admit any given finite automorphism group. This…
Lecture notes in Russian. Topics: the Haar measure (abstract theorems and explicit descriptions for different groups), measures on infinite-dimensional spaces with large natural groups of symmetries (Gaussian measures, Poisson measures,…
We obtain some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particular, the mapping class groups of different closed surfaces can not be measure equivalent. Moreover,…
A tensor space is a vector space equipped with a finite collection of multi-linear forms. In recent years, a rich theory of infinite dimensional tensor spaces has emerged. In this note, we show that a large class of permutation groups can…
Knop constructed a tensor category associated to a finitely-powered regular category equipped with a degree function. In recent work with Harman, we constructed a tensor category associated to an oligomorphic group equipped with a measure.…
In recent work with Harman, we introduced a notion of measure on a class of finite relational structures. In this note, we consider measures on the class of permutations, i.e., finite sets with two total orders. Using a method of Nekrasov,…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…
Raimi's classical theorem establishes a partition of the natural numbers with a remarkable unavoidability property: for every finite coloring of $\mathbb{N}$, there is a color class whose translate meets both parts of the partition in…
In previous work we determined automorphism groups of cyclic algebraic curves defined over fields of any odd characteristic. In this paper we determine parametric equations of families of curves for each automorphism group for such curves.
Counting homomorphisms between cyclic groups is a common exercise in a first course in abstract algebra. A similar problem, accessible at the same level, is to count the number of group homomorphisms from a dihedral group of order $2m$ into…
Given a set equipped with a transitive action of a group, we define the notion of an almost invariant coloring of the set. We consider the mapping class group orbit of a multicurve on a compact surface, and prove that in the case of genus…
We study criteria for the existence of a dense or comeager conjugacy class in the automorphism group of a given measure on the Cantor space. We concentrate on good measures, defined by Akin [\emph{Trans.\ Amer.\ Math.\ Soc.} \textbf{357}…
Endomorphisms of the measure algebra of commutative hypergroups are investigated. We focus on derivations and higher order derivations which are closely related to moment function sequences of higher rank. We describe the exact connection…
We study invariant ergodic measures for quasiperiodically forced circle homeomorphisms and derive that either the system is uniquely ergodic or any such measure is associated to some invariant multigraph.
A connection between representation of compact groups and some invariant ensembles of Hermitian matrices is described. We focus on two types of invariant ensembles which extend the Gaussian and the Laguerre Unitary ensembles. We study them…
The z-measures on partitions originated from the problem of harmonic analysis of linear representations of the infinite symmetric group in the works of Kerov, Olshanski and Vershik (1993, 2004). A similar family corresponding to projective…
In recent work, Rosenbaum and Wagner showed that isomorphism of explicitly listed $p$-groups of order $n$ could be tested in $n^{\frac{1}{2}\log_p n + O(p)}$ time, roughly a square root of the classical bound. The $O(p)$ term is entirely…
We construct a new invariant metric for a compact subgroup of the automorphism group of a domain in complex space. Applications are provided.
We introduce a geometrically natural probability measure on the group of all M\"obius transformations of the circle. Our aim is to study "random" groups of M\"obius transformations, and in particular random two-generator groups. By this we…