On Tensor-Factorisation Problems, I: The Combinatorial Problem

P.M. Neumann, Cheryl Praeger

    Research output: Contribution to journalArticle

    Abstract

    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 of x and y is defined as the rs-multiset {xiyj | 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?
    Original languageEnglish
    Pages (from-to)73-100
    JournalLMS Journal of Computation and Mathematics
    Volume7
    Publication statusPublished - 2004

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