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On Tensor-Factorisation Problems,I: The Combinatorial Problem

Published online by Cambridge University Press:  01 February 2010

Peter M. Neumann  and
Cheryl E. Praeger
Peter M. Neumann
Affiliation:
The Queen's College, Oxford 0X1 4AW, United Kingdom, peter.neumann@queens.ox.ac.uk
Cheryl E. Praeger
Affiliation:
School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia, praeger@maths.uwa.edu.au, http://www.maths.uwa.edu.au/~praeger

Abstract

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A k-multiset is an unordered k-tuple, perhaps with repetitions. If x is an r-multiset {x1, …, xr} and y is an s-multiset {y1, …, ys} with elements from an abelian group A the tensor product x ⊗ y is defined as the rs-multiset {xi yj | 1 ≤ i ≤ r, 1 ≤ j ≤ s}. The main focus of this paper is a polynomial-time algorithm to discover whether a given rs-multiset from A can be factorised. The algorithm is not guaranteed to succeed, but there is an acceptably small upper bound for the probability of failure. The paper also contains a description of the context of this factorisation problem, and the beginnings of an attack on the following division-problem: is a given rs-multiset divisible by a given r-multiset, and if so, how can division be achieved in polynomially bounded time?

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 7 , 2004 , pp. 73 - 100
Copyright
Copyright © London Mathematical Society 2004

References

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