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@article {stembridge-fullycommutative,
    AUTHOR = {Stembridge, John R.},
     TITLE = {On the fully commutative elements of {C}oxeter groups},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {5},
      YEAR = {1996},
    NUMBER = {4},
     PAGES = {353--385},
      ISSN = {0925-9899},
   MRCLASS = {20F55 (05E15)},
  MRNUMBER = {1406459},
MRREVIEWER = {Kimmo Eriksson},
       DOI = {10.1023/A:1022452717148},
       URL = {https://doi.org/10.1023/A:1022452717148},
}

@article {lam-pylyavskyy,
    AUTHOR = {Lam, Thomas and Pylyavskyy, Pavlo},
     TITLE = {Total positivity for loop groups {II}: {C}hevalley generators},
   JOURNAL = {Transform. Groups},
  FJOURNAL = {Transformation Groups},
    VOLUME = {18},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {179--231},
      ISSN = {1083-4362},
   MRCLASS = {22E67},
  MRNUMBER = {3022763},
MRREVIEWER = {Derek Krepski},
       DOI = {10.1007/s00031-013-9208-y},
       URL = {https://doi.org/10.1007/s00031-013-9208-y},
}

@article {lam-thomas,
    AUTHOR = {Lam, Thomas and Thomas, Anne},
     TITLE = {Infinite reduced words and the {T}its boundary of a {C}oxeter
              group},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2015},
    NUMBER = {17},
     PAGES = {7690--7733},
      ISSN = {1073-7928},
   MRCLASS = {20F55 (20F65 20F69)},
  MRNUMBER = {3403997},
MRREVIEWER = {Stefan Witzel},
       DOI = {10.1093/imrn/rnu182},
       URL = {https://doi.org/10.1093/imrn/rnu182},
}

@book {Bourbaki,
    AUTHOR = {Bourbaki, Nicolas},
     TITLE = {Lie groups and {L}ie algebras. {C}hapters 4--6},
    SERIES = {Elements of Mathematics (Berlin)},
      NOTE = {Translated from the 1968 French original by Andrew Pressley},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2002},
     PAGES = {xii+300},
      ISBN = {3-540-42650-7},
   MRCLASS = {17-01 (00A05 20E42 20F55 22-01)},
  MRNUMBER = {1890629},
       DOI = {10.1007/978-3-540-89394-3},
       URL = {https://doi.org/10.1007/978-3-540-89394-3},
}

@article {Proctor,
    AUTHOR = {Proctor, Robert A.},
     TITLE = {Bruhat lattices, plane partition generating functions, and
              minuscule representations},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {5},
      YEAR = {1984},
    NUMBER = {4},
     PAGES = {331--350},
      ISSN = {0195-6698},
   MRCLASS = {17B20 (05A15 05A17)},
  MRNUMBER = {782055},
MRREVIEWER = {S. Milne},
       DOI = {10.1016/S0195-6698(84)80037-2},
       URL = {https://doi.org/10.1016/S0195-6698(84)80037-2},
}

@article {Speyer,
    AUTHOR = {Speyer, David E.},
     TITLE = {Powers of {C}oxeter elements in infinite groups are reduced},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {137},
      YEAR = {2009},
    NUMBER = {4},
     PAGES = {1295--1302},
      ISSN = {0002-9939},
   MRCLASS = {20F55},
  MRNUMBER = {2465651},
MRREVIEWER = {Tom De Medts},
       DOI = {10.1090/S0002-9939-08-09638-X},
       URL = {https://doi.org/10.1090/S0002-9939-08-09638-X},
}

@book {Bjorner-Brenti,
    AUTHOR = {Bj\"{o}rner, Anders and Brenti, Francesco},
     TITLE = {Combinatorics of {C}oxeter groups},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {231},
 PUBLISHER = {Springer, New York},
      YEAR = {2005},
     PAGES = {xiv+363},
      ISBN = {978-3540-442387; 3-540-44238-3},
   MRCLASS = {05-01 (05E15 20F55)},
  MRNUMBER = {2133266},
MRREVIEWER = {Jian-yi Shi},
}

@book {Humphreys,
    AUTHOR = {Humphreys, James E.},
     TITLE = {Reflection groups and {C}oxeter groups},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {29},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1990},
     PAGES = {xii+204},
      ISBN = {0-521-37510-X},
   MRCLASS = {20-02 (20F32 20F55 20G15 20H15)},
  MRNUMBER = {1066460},
MRREVIEWER = {Louis Solomon},
       DOI = {10.1017/CBO9780511623646},
       URL = {https://doi.org/10.1017/CBO9780511623646},
}

@article {lam-pylyavskyy-part1,
    AUTHOR = {Lam, Thomas and Pylyavskyy, Pavlo},
     TITLE = {Total positivity in loop groups, {I}: {W}hirls and curls},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {230},
      YEAR = {2012},
    NUMBER = {3},
     PAGES = {1222--1271},
      ISSN = {0001-8708},
   MRCLASS = {22E67},
  MRNUMBER = {2921179},
MRREVIEWER = {A. L. Onishchik},
       DOI = {10.1016/j.aim.2012.03.012},
       URL = {https://doi.org/10.1016/j.aim.2012.03.012},
}

@incollection {Tits-words,
    AUTHOR = {Tits, Jacques},
     TITLE = {Le probl\`eme des mots dans les groupes de {C}oxeter},
 BOOKTITLE = {Symposia {M}athematica ({INDAM}, {R}ome, 1967/68), {V}ol. 1},
     PAGES = {175--185},
 PUBLISHER = {Academic Press, London},
      YEAR = {1969},
   MRCLASS = {20.10},
  MRNUMBER = {0254129},
MRREVIEWER = {J. E. Humphreys},
}
		
@misc{arxiv-version,
       author = {{Gaetz}, Christian and {Gao}, Yibo},
        title = "{Minimal elements for the limit weak order on affine Weyl groups}",
        eprint = {2101.10230},
        eprinttype={arxiv},
        year={2021},
}