Related papers: Analysing flag-transitive point-imprimitive 2-desi…
The notions of symbolic matrix system and $\lambda$-graph system for a subshift are generalizations of symbolic matrix and $\lambda$-graph (= finite symbolic matrix) for a sofic shift respectively ([Doc. Math. 4(1999), 285-340]). M. Nasu…
A digraph is $s$-arc-transitive if its automorphism group is transitive on directed paths with $s$ edges, that is, on $s$-arcs. Although infinite families of finite $s$-arc transitive digraphs of arbitrary valency were constructed by the…
Let $\pi : X\to \Lambda$ be a flat family of smooth complex projective varieties parameterized by a smooth quasi-projective variety $\Lambda$, and let $f: X\to X$ be a family of automorphisms with positive topological entropy. Suppose…
Let $G$ be a transitive permutation group of degree $n$. We say that $G$ is $2'$-elusive if $n$ is divisible by an odd prime, but $G$ does not contain a derangement of odd prime order. In this paper we study the structure of quasiprimitive…
Following a general program of studying limits of discrete structures, and motivated by the theory of limit objects of converge sequences of dense simple graphs, we study the limit of graph sequences such that every edge is labeled by an…
In the first part of this paper we study geometric formality for generalized flag manifolds, including full flag manifolds of exceptional Lie groups. In the second part we deal with the problem of the classification of invariant almost…
Consider a complete flag $\{0\} = C_0 < C_1 < \cdots < C_n = \mathbb{F}^n$ of one-point AG codes of length $n$ over the finite field $\mathbb{F}$. The codes are defined by evaluating functions with poles at a given point $Q$ in points…
In the last two decades new techniques emerged to construct valuations on an infinite division ring $D,$ given a normal subgroup $N\subseteq D$ of finite index. These techniques were based on the commuting graph of $D^{\times}/N$ in the…
This paper studies the existence of finite non-Desarguesian flag-transitive projective plane, giving necessary conditions in terms of polynomial equations over finite fields of characteristic $3$. This sheds light on the longstanding…
Finite projective planes are constructed using groups that satisfy simple-looking conditions. The resulting projective planes include many known planes and possibly new ones, and are precisely those having a collineation group fixing a flag…
This paper begins the classification of all edge-primitive 3-arc-transitive graphs by classifying all such graphs where the automorphism group is an almost simple group with socle an alternating or sporadic group, and all such graphs where…
We classify GL(2,R) invariant point markings over components of strata of Abelian differentials. Such point markings exist only when the component is hyperelliptic and arise from marking Weierstrass points or two points exchanged by the…
We present some results on the harmonious colorings of the Levi graph of a $2$-design, focusing on Steiner $2$-designs. It is easily seen that the harmonious chromatic number of such a Levi graph is at least the number of points of the…
In this paper, we propose a topological classification of points for 2D discrete binary images. This classification is based on the values of the calculus of topological numbers. Six classes of points are proposed: isolated point, interior…
Many interesting geometric structures can be described as regular infinitesimal flag structures, which occur as the underlying structures of parabolic geometries. Among these structures we have for instance conformal structures, contact…
The sets of primitive, quasiprimitive, and innately transitive permutation groups may each be regarded as the building blocks of finite transitive permutation groups, and are analogues of composition factors for abstract finite groups. This…
In this paper we study the structure of $k$-transitive closures of directed paths and formulate several properties. Concept of $k$-transitive orientation generalize the traditional concept of transitive orientation of a graph.
We survey partial geometric designs and investigate their concurrences of points. The concurrence matrix of a design, which encodes the concurrences of pairs of points, can be used in the classification of designs in some extent. An…
Unitary graphs are arc-transitive graphs with vertices the flags of Hermitian unitals and edges defined by certain elements of the underlying finite fields. They played a significant role in a recent classification of a class of…
In this paper, we introduce a family of tetravalent graphs called propeller graphs, denoted by $Pr_{n}(b,c,d)$. We then produce three infinite subfamilies and one finite subfamily of arc-transitive propeller graphs, and show that all such…