The factorization of the permanent of a matrix with minimal rank in prime characteristic

David Glynn

    Research output: Contribution to journalArticle

    Abstract

    It is known that any square matrix A of size n over a field of prime characteristic p that has rank less than n/(p - 1) has a permanent that is zero. We give a new proof involving the invariant X p . There are always matrices of any larger rank with non-zero permanents. It is shown that when the rank of A is exactly n/(p - 1), its permanent may be factorized into two functions involving X p .

    Original languageEnglish
    Pages (from-to)175-177
    Number of pages3
    JournalDesigns Codes and Cryptography
    Volume62
    Issue number2
    DOIs
    Publication statusPublished - 2012

    Keywords

    • Matrix
    • Permanent
    • Prime characteristic
    • Rank

    Fingerprint Dive into the research topics of 'The factorization of the permanent of a matrix with minimal rank in prime characteristic'. Together they form a unique fingerprint.

  • Cite this