Partee (1986) claimed without proof that the function BE is the only homomorphism that makes the Partee triangle commute. This paper shows that this claim is incorrect unless “homomorphism” is understood as “complete homomorphism.” It also shows that BE and A are the inverses of each other on certain natural assumptions.

Representation varieties of closed surface groups into SL(n,R) have been studied extensively by Hitchin and Labourie, and the dimension of a certain distinguished component of the variety was obtained by Hitchin using Higgs bundles. Here we determine the corresponding dimension for representations of triangle groups into SL(n,R), generalising some earlier work of Choi and Goldman in the case n ...

We investigate asphericity of the relative group presentation 〈G, t | atbtctdtet = 1〉 and prove it aspherical provided the subgroup of G generated by {ab−1, bc−1, cd−1, de−1} is neither finite cyclic nor a finite triangle group. We also prove a similar result for the closely related relative group presentation 〈G, s, t | αsβsγt = 1 = δtεtζs−1〉.

This paper introduces a new system for classifying scholarly journals in terms of their degree of 'application orientation'. The method extends earlier models and journals classification systems that were designed to tackle the crude duality

For a given triangle there are many points associated with the triangle that lie in its interior; examples include the incenter (which can be found by the intersection of the angle bisectors) and the centroid (which can be found by the intersection of the medians). Using this point one can naturally subdivide the triangle into either three or six “daughter” triangles. We can then repeat the sam...

In this paper we obtain structure results for the largest finite generalized triangle group that has been called the Rosenberger Monster. These structure results are motivated by their application for finding various homological functors for this group.

In this paper, we consider the planar Sierpinski measures μM,D generated by an expanding integer matrix M ∈ M2(Z) and the digit set D = {( 0 0 )

A complex hyperbolic triangle group is the group of complex hyperbolic isometries generated by complex involutions fixing three complex lines in complex hyperbolic space. Such a group is called equilateral if there is an isometry of order three that cyclically permutes the three complex lines. We consider equilateral triangle groups for which the product of each pair of involutions and the prod...

0. Introduction The Genocchi numbers appear in many different contexts (see e.g. [1,4,5,7,6,14,20]). Probably the most well-known definition uses the Seidel triangle 155 155 17 17 155 310 3 3 17 34 138 448 1 1 3 6 14 48 104 552 1 1 1 2 2 8 8 56 56 608 By definition, the triangle is formedby the numbers gk,n (k is the number of a row counted frombottom to top and n is the number of a column from...