In the recent paper (Casselman, 2001) I described how a number of ideas due to Fokko du Cloux and myself could be incorporated into a reasonably efficient program to carry out multiplication in arbitrary Coxeter groups. At the end of that paper I discussed how this algorithm could be used to build the reflection table of minimal roots, which could in turn form the basis of a much more efficient...

A (partial) Latin square is a table of multiplication of a (partial) quasigroup. Multiplication of a (partial) quasigroup may be considered as a set of triples. We give a necessary and sufficient condition when a set of triples is a quotient of a (partial) Latin square.

We study Boolean routing on Cayley networks. Let K (M G) denote the Kolmogorov complexity of the multiplication table of a group G of order n. We show that O(maxfd logn; K (M G)g) memory bits per local router (hence a total of O(n maxfd logn; K (M G)g) memory bits) are suucient to do Boolean routing on the Cayley network constructed from the group G and a set of d generators. It is a consequenc...

Traditionally, many ethnic groups had their own versions of arithmetic algorithms. Nowadays, most of these algorithms are studied mostly as pedagogical curiosities, as an interesting way to make arithmetic more exciting to the kids: by applying to their patriotic feelings – if they are studying the algorithms traditionally used by their ethic group – or simply to their sense of curiosity. Somew...

the non-split extension group $overline{g} = 5^3{^.}l(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in ly. the group $overline{g}$ in turn has l(3,5) and $5^2{:}2.a_5$ as inertia factors. the group $5^2{:}2.a_5$ is of order 3 000 and is of index 124 in l(3,5). the aim of this paper is to compute the fischer-clifford matrices of $overline{g}$, which together with associated parti...

in this paper we first construct the non-split extension $overline{g}= 2^{6} {^{cdot}}sp(6,2)$ as a permutation group acting on 128 points. we then determine the conjugacy classes using the coset analysis technique, inertia factor groups and fischer matrices, which are required for the computations of the character table of $overline{g}$ by means of clifford-fischer theory. there are two inerti...

A look-up table based transform that has the properties of being both reversible and multiplication-free is proposed in this report. While the method can be applied to any arbitrary orthonormal matrix transform, the performance of the RGB to YUV color transform is used to evaluate this approach. The performance is found to be nearly identical to what is achievable by the optimum KLT. In order t...

This paper reveals a number of learning activities emerging from a spreadsheetgenerated multiplication table. These activities are made possible by using such features of the software as conditional formatting, circular referencing, calculation through iteration, scroll bars, and graphing. The paper is a reflection on a mathematics content course designed for prospective elementary teachers usi...