Related papers: Unifom chains of small transfinite rank

We show that every definable group G in an o-minimal structure is definably finitely generated. That is, G contains a finite subset that is not included in any proper definable subgroup. This provides another proof, and a generalization to…

In this paper, we first determine the minimum possible size of an Fq-linear set of rank k in PG(1, q^n). We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a…

We show that a finite collection of stable subgroups of a finitely generated group has finite height, finite width and bounded packing. We then use knowledge about intersections of conjugates to characterize finite families of…

Finite distributive lattices whose join-meet ideals are of K\"onig type will be classified. Furthermore, a class of polyominoes whose polyomino ideals are of K\"onig type will be studied.

This article began as a study of the structure of infinite permutation groups G in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point…

Upper bounds on projective rigidity of each homogeneously embedded homogeneous variety are determined; and a new, invariant characterization of the Fubini forms is given.

We show that all permutations in $S_n$ can be generated by affine unicritical polynomials. We use the $\operatorname{PGL}$ group structure to compute the cycle structure of permutations with low Carlitz rank. The tree structure of the group…

Let $A$ be a simple, exact, separable, unital $C^*$-algebra and let $\alpha \colon G \rightarrow Aut(A)$ be an action of a finite group $G$ with the weak tracial Rokhlin property. We show that every trace on $A \rtimes_{\alpha} G$ is…

We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains.

In this article, we obtain quasiconformal extensions of some classes of conformal maps defined either on the unit disc or on the exterior of it onto the extended complex plane. Some of these extensions have been obtained by constructing…

Lusztig conjectured that the almost characters of a finite reductive group are up to a scalar the same as the characteristic functions of the rational character sheaves defined on the corresponding algebraic group. We propose in this paper…

We classify the finite connected-homogeneous digraphs, as well as the infinite such digraphs with precisely one end. This completes the classification of all the locally finite connected-homogeneous digraphs.

We describe all finite subsemigroups of a free left regular band of infinite rank. Moreover, we show applications of this result in algebraic geometry and model theory.

We extend Matui's notion of almost finiteness to general etale groupoids and show that the reduced groupoid C*-algebras of minimal almost finite groupoids have stable rank one. The proof follows a new strategy, which can be regarded as a…

Let $S=(C \times D)/G$ be a surface isogenous to a higher product of unmixed type with $p_g=q=0$, $G=(\mathbb{Z}/2)^3$ or $(\mathbb{Z}/2)^4$. We construct exceptional sequences of maximal length and quasiphantom categories on $S$.

The small object argument is a transfinite construction which, starting from a set of maps in a category, generates a weak factorisation system on that category. As useful as it is, the small object argument has some problematic aspects: it…

We introduce a family of natural normalized Loewner chains in the unit ball, which we call "ger\"aumig"---spacious---which allow to construct, by means of suitable variations, other normalized Loewner chains which coincide with the given…

This work investigates the rank properties of $A^+(B_n)$, the additive semigroup reduct of affine near-semiring over Brandt semigroup $B_n$. In this connection, this work reports the ranks $r_1$, $r_2$, $r_3$ and $r_5$ of $A^+(B_n)$ and…

Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…

We show that the existence of a Suslin tree does not necessarily imply that there are uncountable minimal linear orders other than $\omega_1$ and $-\omega_1$, answering a question of J. Baumgartner. This is done by a Jensen-type iteration,…