We construct a finitely presented torsion-free simple group Σ0, acting cocompactly on a product of two regular trees. An infinite family of such groups has been introduced by Burger-Mozes ([2, 4]). We refine their methods and get Σ0 as an index 4 subgroup of a group Σ < Aut(T12)×Aut(T8) presented by 10 generators and 24 short relations. For comparison, the smallest virtually simple group of [4,...

Array statements are often used to express data-parallelism in scientiic languages such as Fortran 90 and High Performance Fortran. In compiling array statements for a distributed-memory machine, eecient generation of communication sets and local index sets is important. We show that for arrays distributed block-cyclically on multiple processors, the local memory access sequence and communicati...

The notions of ultrametric distances and cyclic valuations appear when the set of values of the distance map is a cyclically ordered set. These structures can be described as subspaces of cartesian products. In this paper we characterize existentially equivalence between cyclically ultrametric spaces, as well as existentially equivalence between generalized ultrametric spaces. We also describe ...

Barot, Geiss and Zelevinsky define a notion of a “cyclically orientable graph” and use it to devise a test for whether a cluster algebra is of finite type. Barot, Geiss and Zelivinsky’s work leaves open the question of giving an efficient characterization of cyclically orientable graphs. In this paper, we give a simple recursive description of cyclically orientable graphs, and use this to give ...