 
Summary: AAECC 7, 5357 (1996)
AAECCApplicableAlgebrain
Engineering, Communication
andComputing
9 SpringerVerlag1996
Invariants of S4and the Shape of Sets of Vectors
Helmer Aslaksen 1, ShihPing Chan2, Tor Gulliksen3
1 Department of Mathematics, National University of Singapore, Singapore 0511, Republic of
Singapore, email: aslaksen@math.nus.sg
z Department of Mathematics, National University of Singapore, Singapore 0511, Republic of
Singapore, email: matchansp@math.nus.sg
3 Department of Mathematics, University ofOslo, P.O. Box 1053,Blindern, 0316Oslo, Norway,
email:torg@math.uio.no
Received October 7, 1993;revised version November 28, 1994
Abstract. We study a representation of S, that is related to the shape of sets of
vectors in ~". We want to determine the invariants of this representation, and obtain
a complete description for the case of S,.
Keywords: Invariants of finite groups, Shape of sets of vectors.
1 Introduction
When studying the shape of a set of n vectors in W", we are led to consider the
