Concepedia

Bruhat Order

Bruhat Order is a partial order on the elements of a Coxeter group, particularly the symmetric group, wherein one element is less than another if it can be obtained by a sequence of simple transpositions that reduce the number of inversions, thus distinguishing it from other partial orders on permutations by its specific relation to the group's Bruhat decomposition and its connection to the geometry of flag varieties.

137

Publications

6.9K

Citations

136

Authors

103

Institutions

Publications per year

2017–2026

7

Variants

Bruhat Ordering

Parents

Publications

137

Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property

Richard P. Stanley · SIAM Journal on Algebraic and Discrete Methods · 1980 · 450 citations

, , +9

Double Bruhat cells and total positivity

Sergey Fomin, Andrei Zelevinsky · Journal of the American Mathematical Society · 1999 · 362 citations · Full text

, , +10

Gröbner geometry of Schubert polynomials

Allen Knutson, Ezra Miller · Annals of Mathematics · 2005 · 303 citations · Full text

, , +15

Some characterizations of Bruhat ordering on a Coxeter group and determination of the relative M�bius function

Vinay V. Deodhar · Inventiones mathematicae · 1977 · 255 citations

, , +5

Posets, Regular CW Complexes and Bruhat Order

Anders Björner · European Journal of Combinatorics · 1984 · 253 citations

, , +9

1–5 of 137

Authors

136

  1. FS
    Frank Sottile

    Texas A&M University, United States

    7 publications · 255 citations

    7

    h-index

  2. CL
    Cristian Lenart

    University at Albany, State University of New York, United States

    6 publications · 238 citations

    6

    h-index

  3. LE
    Lex E. Renner

    Western University, Canada

    6 publications · 256 citations

    6

    h-index

  4. AH
    Axel Hultman

    KTH Royal Institute of Technology, Sweden

    5 publications · 140 citations

    5

    h-index

  5. VV
    Vinay V. Deodhar

    Indiana University Bloomington, United States

    5 publications · 758 citations

    5

    h-index

1–5 of 136

Institutions

103

  1. Massachusetts Institute of Technology

    Cambridge, United States

    11 h-index

    14 publications

    1.3K citations

  2. KTH Royal Institute of Technology

    Stockholm, Sweden

    10 h-index

    13 publications

    356 citations

  3. University of Michigan

    Ann Arbor, United States

    8 h-index

    11 publications

    329 citations

  4. University of Wisconsin–Madison

    Madison, United States

    7 h-index

    7 publications

    189 citations

  5. Centre National de la Recherche Scientifique

    Paris, France

    6 h-index

    7 publications

    217 citations

  6. University at Albany, State University of New York

    Albany, United States

    5 h-index

    5 publications

    209 citations

  7. Western University

    London, Canada

    4 h-index

    4 publications

    115 citations

  8. North Carolina State University

    Raleigh, United States

    4 h-index

    4 publications

    113 citations

1–8 of 103

Venues

  1. Journal of Algebraic Combinatorics

    10 publications · 344 citations

    10

    h-index

  2. Journal of Algebra

    10 publications · 631 citations

    10

    h-index

  3. The Electronic Journal of Combinatorics

    8 publications · 271 citations

    9

    h-index

  4. Journal of Combinatorial Theory Series A

    6 publications · 185 citations

    6

    h-index

  5. Transactions of the American Mathematical Society

    TRAN · 6 publications · 169 citations

    6

    h-index

1–5