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Bibliographic Metadata

  • Title
    Invariants for permutation-Hermite equivalence and critical dimension groups
  • Author
    Handelman, David ; Handelman, David Eli
  • Is part of
    Münster Journal of Mathematics, Issue Münster Journal of Mathematics, page 49-156
  • Published
    2018
  • Language
    English
  • Document type
    Journal Article
  • URN
    urn:nbn:de:hbz:6-87109580116 
  • DOI
    10.17879/87109579816 
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Abstract
  • Motivated by classification, up to order isomorphism, of dense subgroups of Euclidean space that are free of minimal rank, we obtain apparently new invariants for an equivalence relation (intermediate between Hermite and Smith) on integer matrices. These then participate in the classification of the dense subgroups. The same equivalence relation has appeared before, in the classification of lattice simplices. We discuss this equivalence relation (called permutation-Hermite), obtain fairly fine invariants for it, and have density results, and some formulas counting the numbers of equivalence classes for fixed determinant.
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