• DocumentCode
    1232303
  • Title

    On the generation of d-ordered sets: a proof based on determinant theory

  • Author

    Weinberg, Louis

  • Author_Institution
    City Coll. of New York, NY, USA
  • Volume
    39
  • Issue
    5
  • fYear
    1992
  • fDate
    5/1/1992 12:00:00 AM
  • Firstpage
    415
  • Lastpage
    418
  • Abstract
    A simple proof of the theorem of determinants that yields d -ordered sets is given. Nothing more complicated than the Laplacian expansion of a determinant is used in the proof, which consists essentially of two parts. First a bordered determinant is used to yield the necessary determinantal equation. Then, transpositions of columns bring the minors in the equation into the required form so that they satisfy the conditions for a d-ordered set
  • Keywords
    matrix algebra; set theory; Laplacian expansion; bordered determinant; columns; d-ordered sets; determinant theory; transpositions; Application software; Circuits; Cities and towns; Computer science; Cryptography; Geometry; Laplace equations; Mathematics; Multidimensional systems; Sorting;
  • fLanguage
    English
  • Journal_Title
    Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    1057-7122
  • Type

    jour

  • DOI
    10.1109/81.139292
  • Filename
    139292
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1232303