Denote by G the set of triples (Γ, X,B), where Γ is a finite X-symmetric graph of valency val(Γ) ≥ 1, B is a nontrivial X-invariant partition of V (Γ) such that ΓB, the quotient graph of Γ with respect to B, is nonempty and Γ is not a multicover of ΓB. In this article, for any given X-symmetric graph Σ, we aim to give a sufficient and necessary condition for the existence of (Γ, X,B) ∈ G, such ...

Abstract We consider a finite, connected and simple graph Γ that admits vertex-transitive group of automorphisms

In this article, we investigate symmetric $(v,k,\lambda)$ designs $\mathcal{D}$ with $\lambda$ prime admitting flag-transitive and point-primitive automorphism groups $G$. We prove that if $G$ is an almost simple group socle a finite of Lie type, then either the point-hyperplane design projective space $\mathrm{PG}_{n-1}(q)$, or it parameters $(7,4,2)$, $(11,5,2)$, $(11,6,3)$ $(45,12,3)$.

A family of sets is said to be symmetric if its automorphism group is transitive, and intersecting if any two sets in the family have nonempty intersection. Our purpose here is to study the following question: for n, k ∈ N with k ≤ n/2, how large can a symmetric intersecting family of k-element subsets of {1, 2, . . . , n} be? As a first step towards a complete answer, we prove that such a fami...

A go/no-go procedure with compound stimuli typically establishes emergent behavior that parallels in structure and typical outcome that of conventional tests for symmetric, transitive, and equivalence relations in normally capable adults. The present study employed a go/no-go compound stimulus procedure with pigeons. During training, pecks to two-component compounds A1B1, A2B2, B1C1, and B2C2 w...

We review key mathematical concepts used in the theory of Statistical Shape Analysis (SSA). The treatment is elementary and aims at providing a brief guide to a large number of results and ideas which are dispersed over an also very large literature on Non-Euclidean Geometry, Differential Geometry, and Topology. The goal is to provide an introduction to the ideas SSA touches in these areas to r...

We study the notion of weak dividing introduced by S. Shelah. In particular we prove that T is stable iff weak dividing is symmetric. In order to study simple theories Shelah originally defined weak dividing in [6] . This notion is overshadowed by that of dividing, as the first author proved that dividing is the right well-behaved notion for simple theories [2],[3],[5],and [4]. However Dolich’s...

Periodic and quasi-periodic orbits of the n-body problem are critical points of the action functional constrained to the Sobolev space of symmetric loops. Variational methods yield collisionless orbits provided the group of symmetries fulfills certain conditions (such as the rotating circle property). Here we generalize such conditions to more general group types and show how to constructively ...

An n×n matrix is called an N 0 -matrix if all principal minors are non-positive and each entry is non-positive. In this paper, we study the partial non-combinatorially symmetric N 0 -matrix completion problems if the graph of its specified entries is a transitive tournament or a double cycle. In general, these digraphs do not have N 0 -completion. Therefore, we have given sufficient conditions ...