This paper gives a sampler on an emerging area of research and applications, namely, computational symmetry. The introduction of computers poses challenging tasks for machine representation and reasoning about symmetry and group theory. We demonstrate, through three concrete applications, the power, the difficulties and feasibility of using symmetry and group theory on computers. A computationa...

Graduate Students C. Coelho, Research Assistant (Graduated), EECS, B. Kim, Research Assistant, S. Kuo, Research Assistant (Graduated), EECS, J.H. Lee, Research Assistant (Graduated), EECS, L. Proctor, Research Assistant, ME, H. Reid, Research Assistant, Physics, L.H. Tan, SMA Student, D. V. Le, SMA joint postdoctoral student, D. Vasilyev, Research Assistant (Graduated), EECS, L. Zhang, Research...

Generic case complexity has originated about a decade ago in combinatorial group theory [10, 2]. This area has long computational traditions with many fundamental problems being algorithmic in nature. It has been shown that most computational problems in infinite group theory are recursively undecidable. However, it was also observed that decision algorithms, sometimes very naive ones, exist fo...

This paper gives a sampler on an emerging area of research and applications, namely, computational symmetry. The introduction of computers poses challenging tasks for machine representation and reasoning about symmetry and group theory. We demonstrate, through three concrete applications, the power, the difficulties and feasibility of using symmetry and group theory on computers. A computationa...

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...

we present the basic results on the representation theory of the alternating groups. our approach is based on clifford theory.

Consciousness as stated by Chalmers [1] is anything that we experience, from perceiving the color of red, depth thought, smell a flower, sound guitar, pleasure orgasms to agony pain.