Groups can be studied using methods from diierent elds such as combina-torial group theory or string rewriting. Recently techniques from Grr obner basis theory for free monoid rings (non-commutative polynomial rings) respectively free group rings have been added to the set of methods due to the fact that monoid and group presentations (in terms of string rewriting systems) can be linked to spec...

Abstract In this paper, we are interested in the asymptotic enumeration of Cayley graphs. It has previously been shown that almost every digraph smallest possible automorphism group: is, it is a digraphical regular representation (DRR). approach corresponding question for undirected The situation complicated by fact there two infinite families groups do not admit any graphical (GRR). strategy d...

We study U–duality symmetries of toroidally compactified M theory from the membrane worldvolume point of view. This is done taking the most general set of bosonic background fields into account. Upon restriction to pure moduli backgrounds, we are able to find the correct U–duality groups and moduli coset parameterizations for dimensions D > 6 as symmetries of the membrane worldvolume theory. In...

The nature of κ-symmmetry transformations is examined for p-branes embedded in a class of coset superspaces G/H, where G is an appropriate supergroup and H is the Lorentz subgroup. It is shown that one of the conditions δZ EM a = 0 which characterizes κ-symmetry transformations arises very naturally if they are implemented in terms of a right action of a subgroup of the supergroup G on the supe...

Abstract Following the paradigm on the sphere, we begin the study of irrational conformal field theory (ICFT) on the torus. In particular, we find that the affine-Virasoro characters of ICFT satisfy heat-like differential equations with flat connections. As a first example, we solve the system for the general g/h coset construction, obtaining an integral representation for the general coset cha...

The author of this book, Professor Shinsaku Fujita, has had a long and productive research career as a chemist, both in industry and in academic research laboratories. This is his fourth book, which builds on the theory developed in the others while minimizing overlap. The author states that the purpose of this book is to disambiguate vocabulary terms used in stereochemistry by introducing more...

We define a graph as orbital regular if there is a subgroup of its automorphism group that acts regularly on the set of edges of the graph as well as on all its orbits of ordered pairs of distinct vertices of the graph. For these graphs there is an explicit formula for the edgeforwarding index, an important traffic parameter for routing in interconnection networks. Using the arithmetic properti...

The superconformal structure of coset superspaces with AdSm × Sn geometry of bosonic subspaces is studied. It is shown, in particular, that the conventional superspace extensions of the coset manifolds AdS2 × S2, AdS3 × S3 and AdS5 × S5, which arise as solutions of corresponding D = 4, 6, 10 supergravities and have been extensively studied in connection with AdS/CFT correspondence, are not supe...

This note contains a report of a proof by computer that the Fi-bonacci group F (2; 9) is automatic. The automatic structure can be used to solve the word problem in the group. Furthermore, it can be seen directly from the word-acceptor that the group generators have innnite order, which of course implies that the group itself is innnite. They have been favourite test examples in combinatorial g...

We study the double cosets of a Lie group by a compact Lie subgroup. We show that a Weil formula holds for double coset Lie hypergroups and show that certain representations of the Lie group lift to representations of the double coset Lie hypergroup. We characterize smooth (analytic) vectors of these lifted representations.