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Let $D=(V(D), A(D))$ be a digraph and $k \ge 2$ an integer. We say that $D$ is $k$-quasi-transitive if for every directed path $(v_0, v_1,..., v_k)$ in $D$, then $(v_0, v_k) \in A(D)$ or $(v_k, v_0) \...
Amenable, transitive and faithful actions of groups acting on trees     Amenable  transitive  faithful actions  groups  trees       font style='font-size:12px;'> 2012/3/1
We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such...
Experimenting with Transitive Verbs in a DisCoCat     Transitive Verbs  DisCoCat  Experimenting  Category Theory       font style='font-size:12px;'> 2011/10/8
Abstract: Formal and distributional semantic models offer complementary benefits in modeling meaning. The categorical compositional distributional (DisCoCat) model of meaning of Coecke et al. (arXiv:1...
Abstract: This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary diffe...
Transitive conformal holonomy groups     conformal holonomy groups  Differential Geometry       font style='font-size:12px;'> 2011/8/24
Abstract: For $(M,[g])$ a conformal manifold of signature $(p,q)$ and dimension at least three, the conformal holonomy group $\mathrm{Hol}(M,[g]) \subset O(p+1,q+1)$ is an invariant induced by the can...
Abstract: n [D. de Caen, E.R. van Dam. Fissioned triangular schemes via the cross-ratio, {Europ. J. Combin.}, 22 (2001) 297-301], de Caen and van Dam constructed a fission scheme $\FT(q+1)$ of the tri...
Transitive Sets and Cyclic Quadrilaterals      Transitive Sets  Cyclic Quadrilaterals        font style='font-size:12px;'> 2011/2/28
Motivated by some questions in Euclidean Ramsey theory, our aim in this note is to show that there exists a cyclic quadrilateral that does not embed into any transitive set (in any dimension). We show...
Transitive Sets in Euclidean Ramsey Theory      Transitive  Euclidean Ramsey Theory        font style='font-size:12px;'> 2011/1/19
A finite set X in some Euclidean space Rn is called Ramsey if for any k there is a d such that whenever Rd is k-coloured it contains a monochromatic set congruent to X. This notion was introduced by E...
A group G acts infinitely transitively on a set Y if for every positive integer m, its action is m-transitive on Y . Given a real affine algebraic variety Y of dimension greater than or equal to 2, ...
On the base size of a transitive group with solvable point stabilizer     the base size  transitive group        font style='font-size:12px;'> 2010/11/23
We prove that the base size of a transitive group $G$ with solvable point stabilizer is not greater than $k$ provided the same statement holds for every group of $G$-induced automorphisms of each nona...
Topological transitive Abelian subgrouns of GL(n,R)     Topological  Abelian subgrouns of GL(n,R)       font style='font-size:12px;'> 2010/11/8
We give a complete characterization of abelian subgroups of GL(n, R) with a locally dense (resp. dense) orbit in R^n. For finitely generated subgroups, this characterization is explicit and it is used...
Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p~k (k ≥ 1), and let A be the full automorphism group of X. In this paper, we prove that the stabilizer Av of a vertex ...
Barely Transitive Groups     Locally finite group  barely transitive group  infinite permutation group       font style='font-size:12px;'> 2010/2/26
This is a survey article on barely transitive groups. It also involves some recent results in the case of a non-locally finite barely transitive group.
We give a group theoretic proof of the splitting of sharply 2-transitive groups of characteristic 3.
On Torsion-Free Barely Transitive Groups     Barely transitive  commensurable       font style='font-size:12px;'> 2010/3/1
B. Hartley asked the following question: Does there exist a torsion free barely transitive group? Existence of torsion free simple barely transitive group is also unknown. We answer the latter questio...

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