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Invariants for permutation-Hermite equivalence and critical dimension groups

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.

Titel: Invariants for permutation-Hermite equivalence and critical dimension groups
Verfasser: Handelman, David GND
Organisation: FB 10: Mathematik und Informatik
Dokumenttyp: Artikel
Medientyp: Text
Erscheinungsdatum: 2018
Publikation in MIAMI: 25.10.2018
Datum der letzten Änderung: 16.04.2019
Zeitschrift/Periodikum: Münster Journal of Mathematics / 11 (2018), S. 49 - 156
Verlag/Hrsg.: Mathematisches Institut (Universität Münster)
Fachgebiete: Mathematik
Sprache: Englisch
Format: PDF-Dokument
URN: urn:nbn:de:hbz:6-87109580116
Permalink: https://nbn-resolving.org/urn:nbn:de:hbz:6-87109580116
DOI: 10.17879/87109579816
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