TP 2 = Bruhat

It is shown that the Bruhat partial order on permutations is equivalent to a certain natural partial order induced by TP 2 matrices and that a positive matrix is TP 2 if (and only if) it satisfies certain inequalities induced by Bruhat order.

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Published inDiscrete mathematics Vol. 310; no. 10; pp. 1627 - 1628
Main Authors Johnson, C.R., Nasserasr, S.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2010
Subjects
[formula omitted] matrix
Bruhat order
Permutations
Total positivity
TP 2 matrix
Permutations
Total positivity
Bruhat order
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Abstract It is shown that the Bruhat partial order on permutations is equivalent to a certain natural partial order induced by TP 2 matrices and that a positive matrix is TP 2 if (and only if) it satisfies certain inequalities induced by Bruhat order.
AbstractList It is shown that the Bruhat partial order on permutations is equivalent to a certain natural partial order induced by TP 2 matrices and that a positive matrix is TP 2 if (and only if) it satisfies certain inequalities induced by Bruhat order.
Author Johnson, C.R.
Nasserasr, S.
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crossref_primary_10_1080_00927872_2015_1087011
Cites_doi 10.1016/j.laa.2007.01.012
10.37236/1847
10.1137/0605057
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Permutations
Total positivity
Bruhat order
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S.M. Fallat, C.R. Johnson, Totally Nonnegative Matrices, Princeton University Press (in press)
Abello, Johnson (b1) 1984; 5
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Björner (10.1016/j.disc.2009.12.021_b2) 2005; vol. 231
10.1016/j.disc.2009.12.021_b4
Fallat (10.1016/j.disc.2009.12.021_b3) 2007; 423
Abello (10.1016/j.disc.2009.12.021_b1) 1984; 5
Drake (10.1016/j.disc.2009.12.021_fr1) 2004; 11
References_xml – volume: 423
  start-page: 420
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  ident: b3
  article-title: Hadamard powers and totally positive matrices
  publication-title: Linear Algebra Appl.
  contributor:
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  publication-title: SIAM J. Algebr. Discrete Methods
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  ident: 10.1016/j.disc.2009.12.021_b3
  article-title: Hadamard powers and totally positive matrices
  publication-title: Linear Algebra Appl.
  doi: 10.1016/j.laa.2007.01.012
  contributor:
    fullname: Fallat
– volume: 11
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  ident: 10.1016/j.disc.2009.12.021_fr1
  article-title: Two new criteria for comparison in the Bruhat order
  publication-title: Electron. J. Combin.
  doi: 10.37236/1847
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    fullname: Drake
– ident: 10.1016/j.disc.2009.12.021_b4
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  ident: 10.1016/j.disc.2009.12.021_b2
  contributor:
    fullname: Björner
– volume: 5
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  ident: 10.1016/j.disc.2009.12.021_b1
  article-title: How large are transitive simple majority domains?
  publication-title: SIAM J. Algebr. Discrete Methods
  doi: 10.1137/0605057
  contributor:
    fullname: Abello
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Snippet It is shown that the Bruhat partial order on permutations is equivalent to a certain natural partial order induced by TP 2 matrices and that a positive matrix...
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SubjectTerms [formula omitted] matrix
Bruhat order
Permutations
Total positivity
Title TP 2 = Bruhat
URI https://dx.doi.org/10.1016/j.disc.2009.12.021
Volume 310
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