@article {ARW,
    AUTHOR = {Ardila, F. and Rinc\'on, F. and Williams, L.},
     TITLE = {Positively oriented matroids are realizable},
   JOURNAL = {J. Eur. Math. Soc. (JEMS)},
  FJOURNAL = {Journal of the European Mathematical Society (JEMS)},
    VOLUME = {19},
      YEAR = {2017},
    NUMBER = {3},
     PAGES = {815--833},
   MRCLASS = {52C40 (05B35 14M15)},
  MRNUMBER = {3612868},
MRREVIEWER = {Joseph E. Bonin},
       DOI = {10.4171/JEMS/680},
}

@article{ABL,
    AUTHOR = {Arkani-Hamed, N. and Bai, Y. and Lam, T.},
     TITLE = {Positive geometries and canonical forms},
   JOURNAL = {J. High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
      YEAR = {2017},
    NUMBER = {11},
     PAGES = {39 pp.},
       DOI = {10.1007/JHEP11(2017)039}
}

@book {abcgpt,
    AUTHOR = {Arkani-Hamed, N. and Bourjaily, J. and Cachazo, F.
	      and Goncharov, A. and Postnikov, A. and Trnka, J.},
     TITLE = {Grassmannian Geometry of Scattering Amplitudes},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2016},
     PAGES = {ix+194},
   MRCLASS = {81-02 (81R05 81R10 81T60)},
  MRNUMBER = {3467729},
MRREVIEWER = {Yasuhiro Abe},
       DOI = {10.1017/CBO9781316091548},
}

@article{Arkani-Hamed-Thomas-Trnka,
    AUTHOR = {Arkani-Hamed, N. and Thomas, H. and Trnka, J.},
     TITLE = {Unwinding the amplituhedron in binary},
   JOURNAL = {J. High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {16 pp.},
       DOI = {10.1007/JHEP01(2018)016}
}

@article {AT,
    AUTHOR = {Arkani-Hamed, N. and Trnka, J.},
     TITLE = {The Amplituhedron},
   JOURNAL = {J. High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
      YEAR = {2014},
    NUMBER = {10},
     PAGES = {33 pp.},
       DOI = {10.1007/JHEP10(2014)030}
}

@article {Bjo,
    AUTHOR = {Bj{\"o}rner, A.},
     TITLE = {Posets, regular {CW} complexes and {B}ruhat order},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {5},
      YEAR = {1984},
    NUMBER = {1},
     PAGES = {7--16},
   MRCLASS = {06A10 (52A25 57Q05)},
  MRNUMBER = {746039},
MRREVIEWER = {Udo Pachner},
       DOI = {10.1016/S0195-6698(84)80012-8},
}

@article {BW,
    AUTHOR = {Bj{\"o}rner, A. and Wachs, M.},
     TITLE = {Bruhat order of {C}oxeter groups and shellability},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {43},
      YEAR = {1982},
    NUMBER = {1},
     PAGES = {87--100},
   MRCLASS = {20H15 (06A10 13F20 14L30 52A43)},
  MRNUMBER = {644668},
MRREVIEWER = {S. Milne},
       DOI = {10.1016/0001-8708(82)90029-9},
}

@article {CGV,
    AUTHOR = {Colin de Verdi\`ere, Y. and Gitler, I. and Vertigan, D.},
     TITLE = {R\'eseaux \'electriques planaires. {II}},
   JOURNAL = {Comment. Math. Helv.},
  FJOURNAL = {Commentarii Mathematici Helvetici},
    VOLUME = {71},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {144--167},
   MRCLASS = {05C10 (05C90 94C99)},
  MRNUMBER = {1371682},
MRREVIEWER = {Martin \AA ~koviera},
       DOI = {10.1007/BF02566413},
}


@article {CIM,
    AUTHOR = {Curtis, E.B. and Ingerman, D. and Morrow, J.A.},
     TITLE = {Circular planar graphs and resistor networks},
   JOURNAL = {Linear Algebra Appl.},
  FJOURNAL = {Linear Algebra and its Applications},
    VOLUME = {283},
      YEAR = {1998},
    NUMBER = {1-3},
     PAGES = {115--150},
   MRCLASS = {05C38 (05C40 05C50 94C05)},
  MRNUMBER = {1657214},
MRREVIEWER = {W.-K. Chen},
       DOI = {10.1016/S0024-3795(98)10087-3},
}

@article {edelman_81,
    AUTHOR = {Edelman, P.H.},
     TITLE = {The {B}ruhat order of the symmetric group is lexicographically
              shellable},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {82},
      YEAR = {1981},
    NUMBER = {3},
     PAGES = {355--358},
   MRCLASS = {06A10 (13H10 14M05 20B99 52A22)},
  MRNUMBER = {612718},
       DOI = {10.2307/2043939},
}

@misc{frieden,
  author      = {Frieden, G.},
  Eprint      = {1706.02844},
  Eprinttype  = {arxiv},
  title       = {Affine Type {$A$} Geometric Crystal on the {G}rassmannian},
  year        = {2017},
}

@article {FS,
    AUTHOR = {Fomin, S. and Shapiro, M.},
     TITLE = {Stratified spaces formed by totally positive varieties},
      NOTE = {Dedicated to William Fulton on the occasion of his 60th
              birthday},
   JOURNAL = {Michigan Math. J.},
  FJOURNAL = {Michigan Mathematical Journal},
    VOLUME = {48},
      YEAR = {2000},
     PAGES = {253--270},
   MRCLASS = {20G20 (05E15 14M15 20F55 20G15)},
  MRNUMBER = {1786489},
MRREVIEWER = {Eugenii Shustin},
       DOI = {10.1307/mmj/1030132717},
}

@misc{GKL,
Author = {Galashin, P. and Karp, S.N. and Lam, T.},
Eprint      = {1707.02010},
Eprinttype  = {arxiv},
Title = {The totally nonnegative {G}rassmannian is a ball},
Year = {2017},
}

@misc{GKLinprep,
Author = {Galashin, P. and Karp, S.N. and Lam, T.},
Eprint      = {1801.08953},
Eprinttype  = {arxiv},
Title = {The totally nonnegative part of {$G/P$} is a ball},
Year = {2018},
}

@book {gantmakher_krein_50,
    AUTHOR = {Gantmaher, F.R. and Kre{\u\i}n, M.G.},
     TITLE = {Oscillyacionye matricy i yadra i malye kolebaniya mehani\v
              ceskih sistem},
      NOTE = {2d ed. Translated into English by A. Eremenko \cite{gantmakher_krein_translation}},
 PUBLISHER = {Gosudarstv. Isdat. Tehn.-Teor. Lit., Moscow-Leningrad},
      YEAR = {1950},
     PAGES = {359 pp.},
   MRCLASS = {45.0X},
  MRNUMBER = {0049462 (14,178e)},
MRREVIEWER = {F. V. Atkinson},
}

@book {gantmakher_krein_translation,
    AUTHOR = {Gantmacher, F. P. and Krein, M. G.},
     TITLE = {Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems},
   EDITION = {Revised},
      NOTE = {Translation based on the 1950 Russian original.
              Edited and with a preface by Alex Eremenko},
 PUBLISHER = {AMS Chelsea Publishing, Providence, RI},
      YEAR = {2002},
     PAGES = {viii+310},
   MRCLASS = {34L05 (15A18 34A30 34B05 45B05 47G10 74H45)},
  MRNUMBER = {1908601},
       DOI = {10.1090/chel/345},
}

@article {Hersh,
    AUTHOR = {Hersh, P.},
     TITLE = {Regular cell complexes in total positivity},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {197},
      YEAR = {2014},
    NUMBER = {1},
     PAGES = {57--114},
   MRCLASS = {20F55 (05E15 06A07 20G20)},
  MRNUMBER = {3219515},
MRREVIEWER = {Mikhail V. Belolipetsky},
       DOI = {10.1007/s00222-013-0480-1},
}

@misc{hersh_kenyon,
Author = {Hersh, P. and Kenyon, R.},
  Eprint      = {1803.06217},
  Eprinttype  = {arxiv},
Title = {Shellability of face posets of electrical networks and the {CW} poset property},
  year        = {2018},
}

@misc {karp_cyclic_shift,
    AUTHOR = {Karp, S.N.},
     TITLE = {Moment curves and cyclic symmetry for positive {G}rassmannians.},
eprinttype = {arxiv},
      year = {2018},
    eprint = {1805.06004}
}

@article{Karp-Williams,
Author = {Karp, S.N. and Williams, L.K.},
Title = {The $m=1$ amplituhedron and cyclic hyperplane arrangements},
Year = {in press},
journal = {Int. Math. Res. Not. IMRN},
doi = {10.1093/imrn/rnx140}
}

@incollection {Kenyon,
    AUTHOR = {Kenyon, R.},
     TITLE = {The {L}aplacian on planar graphs and graphs on surfaces},
 BOOKTITLE = {Current developments in mathematics, 2011},
     PAGES = {1--55},
 PUBLISHER = {Int. Press, Somerville, MA},
      YEAR = {2012},
   MRCLASS = {05C50 (39A70 78A46)},
  MRNUMBER = {3098076},
}

@article {KLS,
    AUTHOR = {Knutson, Allen and Lam, Thomas and Speyer, David E.},
     TITLE = {Positroid varieties: juggling and geometry},
   JOURNAL = {Compos. Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {149},
      YEAR = {2013},
    NUMBER = {10},
     PAGES = {1710--1752},
   MRCLASS = {14M15 (05B35 05E05)},
  MRNUMBER = {3123307},
MRREVIEWER = {Jacopo Gandini},
       DOI = {10.1112/S0010437X13007240},
}

@article {kodama_williams_14,
    AUTHOR = {Kodama, Yuji and Williams, Lauren},
     TITLE = {K{P} solitons and total positivity for the {G}rassmannian},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {198},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {637--699},
   MRCLASS = {35Q53 (13F60 35C08)},
  MRNUMBER = {3279534},
MRREVIEWER = {Amin Esfahani},
       DOI = {10.1007/s00222-014-0506-3},
}

@misc{Lam,
Author = {Lam, T.},
  Eprint      = {1402.6261},
  Eprinttype  = {arxiv},
Title = {Electroid varieties and a compactification of the space of electrical networks},
  year        = {2014},
}

@incollection {LamCDM,
    AUTHOR = {Lam, T.},
     TITLE = {Totally nonnegative {G}rassmannian and {G}rassmann polytopes},
 BOOKTITLE = {Current developments in mathematics, 2014},
     PAGES = {51--152},
 PUBLISHER = {Int. Press, Somerville, MA},
      YEAR = {2016},
   MRCLASS = {14M15 (05C10 52B12 52B40)},
  MRNUMBER = {3468251},
MRREVIEWER = {Aigli Papantonopoulou},
}

@article {Lammatchings,
    AUTHOR = {Lam, T.},
     TITLE = {The uncrossing partial order on matchings is {E}ulerian},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {135},
      YEAR = {2015},
     PAGES = {105--111},
   MRCLASS = {06A07 (05C70 06A06)},
  MRNUMBER = {3366472},
MRREVIEWER = {Robert Brignall},
       DOI = {10.1016/j.jcta.2015.04.004},
}

@article {LP1,
    AUTHOR = {Lam, T. and Pylyavskyy, P.},
     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},
   MRCLASS = {22E67},
  MRNUMBER = {2921179},
MRREVIEWER = {A. L. Onishchik},
       DOI = {10.1016/j.aim.2012.03.012},
}

@incollection {LusIntro,
    AUTHOR = {Lusztig, G.},
     TITLE = {Introduction to total positivity},
 BOOKTITLE = {Positivity in {L}ie theory: open problems},
    SERIES = {De Gruyter Exp. Math.},
    VOLUME = {26},
     PAGES = {133--145},
 PUBLISHER = {de Gruyter, Berlin},
      YEAR = {1998},
   MRCLASS = {20G20 (14P99)},
  MRNUMBER = {1648700},
MRREVIEWER = {Vladimir L. Popov},
}

@incollection {Lus2,
    AUTHOR = {Lusztig, G.},
     TITLE = {Total positivity in reductive groups},
 BOOKTITLE = {Lie theory and geometry},
    SERIES = {Progr. Math.},
    VOLUME = {123},
     PAGES = {531--568},
 PUBLISHER = {Birkh\"auser Boston, Boston, MA},
      YEAR = {1994},
   MRCLASS = {20G20},
  MRNUMBER = {1327548},
       DOI = {10.1007/978-1-4612-0261-5_20},
}

@incollection {Lus3,
    AUTHOR = {Lusztig, G.},
     TITLE = {Total positivity and canonical bases},
 BOOKTITLE = {Algebraic groups and {L}ie groups},
    SERIES = {Austral. Math. Soc. Lect. Ser.},
    VOLUME = {9},
     PAGES = {281--295},
 PUBLISHER = {Cambridge Univ. Press, Cambridge},
      YEAR = {1997},
   MRCLASS = {20G20 (14P99 20G42)},
  MRNUMBER = {1635687},
MRREVIEWER = {Richard Dipper},
}

@misc{marsh_rietsch,
Author = {Marsh, R. and Rietsch, K.},
  Eprint      = {1307.1085},
  Eprinttype  = {arxiv},
Title = {The {$B$}-model connection and mirror symmetry for {G}rassmannians},
  year        = {2013},
}

@unpublished{Pos,
AUTHOR = {Postnikov, A.},
   url = {http://math.mit.edu/~apost/papers/tpgrass.pdf},
 TITLE = {Total positivity, {G}rassmannians, and networks},
  year = {2013},
}

@article {PSW,
    AUTHOR = {Postnikov, A. and Speyer, D. and Williams, L.},
     TITLE = {Matching polytopes, toric geometry, and the totally
              non-negative {G}rassmannian},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {30},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {173--191},
       DOI = {10.1007/s10801-008-0160-1},
}

@phdthesis {Rietsch,
    AUTHOR = {Rietsch, K.},
     TITLE = {Total Positivity and Real Flag Varieties},
 Institution = {Massachusetts Institute of Technology},
      YEAR = {1998},
   MRCLASS = {Thesis},
  MRNUMBER = {2716793},
       URL =
              {http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:0599450},
}

@article {rietsch_private,
	AUTHOR = {Rietsch, K.},
   Note = {Private communication},
      YEAR = {2009},
}

@article {RW,
    AUTHOR = {Rietsch, K. and Williams, L.},
     TITLE = {Discrete {M}orse theory for totally non-negative flag
              varieties},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {223},
      YEAR = {2010},
    NUMBER = {6},
     PAGES = {1855--1884},
   MRCLASS = {57T99 (14M15 20G20 52B22)},
  MRNUMBER = {2601003},
MRREVIEWER = {Julianna Tymoczko},
       DOI = {10.1016/j.aim.2009.10.011},
}

@article {scott,
    AUTHOR = {Scott, R.F.},
     TITLE = {Note on a theorem of {P}rof. {C}ayley's},
   JOURNAL = {Messeng. Math.},
    VOLUME = {8},
      YEAR = {1879},
     PAGES = {155--157},
}

@article {scott_06,
    AUTHOR = {Scott, J.S.},
     TITLE = {Grassmannians and cluster algebras},
   JOURNAL = {Proc. London Math. Soc.},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {92},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {345--380},
   MRCLASS = {14M15 (05E15 16S99 22E46)},
  MRNUMBER = {2205721},
MRREVIEWER = {Eric N. Sommers},
       DOI = {10.1112/S0024611505015571},
}

@inproceedings {sturmfels_88,
    AUTHOR = {Sturmfels, B.},
     TITLE = {Totally positive matrices and cyclic polytopes},
 BOOKTITLE = {Proceedings of the {V}ictoria {C}onference on {C}ombinatorial
              {M}atrix {A}nalysis ({V}ictoria, {BC}, 1987)},
   JOURNAL = {Linear Algebra Appl.},
  FJOURNAL = {Linear Algebra and its Applications},
    VOLUME = {107},
      YEAR = {1988},
     PAGES = {275--281},
     CODEN = {LAAPAW},
   MRCLASS = {52A25 (15A48)},
  MRNUMBER = {960150},
MRREVIEWER = {P. McMullen},
       DOI = {10.1016/0024-3795(88)90250-9},
}

@article {Wil,
    AUTHOR = {Williams, L.K.},
     TITLE = {Shelling totally nonnegative flag varieties},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {609},
      YEAR = {2007},
     PAGES = {1--21},
     CODEN = {JRMAA8},
   MRCLASS = {14M15 (06A07)},
  MRNUMBER = {2350779},
MRREVIEWER = {Julianna Tymoczko},
       DOI = {10.1515/CRELLE.2007.059},
}