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@Article{reading_order,
  author     = {Reading, N.},
  journal    = {Order},
  title      = {Order dimension, strong {B}ruhat order and lattice properties for posets},
  year       = {2002},
  number     = {1},
  pages      = {73--100},
  volume     = {19},
  doi        = {10.1023/A:1015287106470},
  fjournal   = {Order. A Journal on the Theory of Ordered Sets and its Applications},
  mrclass    = {05E15 (06A07 20F55)},
  mrnumber   = {1902662},
  mrreviewer = {Hiroshi Naruse},
}

@Misc{gpw,
  author     = {Galashin, P. and Postnikov, A. and Williams, L.},
  title      = {Higher secondary polytopes and regular plabic graphs},
  year       = {2019},
  eprint     = {1909.05435},
  eprinttype = {arxiv},
}

@Article{kk,
  author   = {Karpman, R. and Kodama, Y.},
  journal  = {Adv. Math.},
  title    = {Triangulations and soliton graphs for totally positive {G}rassmannian},
  year     = {2021},
  issn     = {0001-8708},
  pages    = {107439},
  volume   = {376},
  doi      = {10.1016/j.aim.2020.107439},
  fjournal = {Advances in Mathematics},
  mrclass  = {Prelim},
  mrnumber = {4178912},
}

@misc{dkk,
	AUTHOR = {Danilov, V. I. and Karzanov, A. V. and Koshevoy, G. A.},
	EPRINT = {1810.05517},
	EPRINTTYPE = {arxiv},
	TITLE = {Cubillages on cyclic zonotopes, membranes, and higher separation},
	YEAR = {2018}
}

@Article{dkk-survey,
  author    = {Danilov, V. I. and Karzanov, A. V. and Koshevoy, G. A.},
  journal   = {Russ. Math. Surv.},
  title     = {Cubillages on cyclic zonotopes},
  year      = {2019},
  issn      = {0042-1316},
  number    = {6},
  pages     = {1013--1074},
  volume    = {74},
  doi       = {10.1070/rm9879},
  fjournal  = {Russian Mathematical Surveys},
  mrclass   = {05B45 (05D05 52B12 52B70)},
  mrnumber  = {4036770},
  publisher = {{IOP} Publishing},
}

@incollection {dm-h,
    AUTHOR = {Dimakis, A. and M\"{u}ller-Hoissen, F.},
     TITLE = {K{P} solitons, higher {B}ruhat and {T}amari orders},
 BOOKTITLE = {Associahedra, {T}amari lattices and related structures},
    SERIES = {Prog. Math. Phys.},
    VOLUME = {299},
     PAGES = {391--423},
 PUBLISHER = {Birkh\"{a}user/Springer, Basel},
      YEAR = {2012},
   MRCLASS = {35Q53 (05C05 06B99 35C08)},
  MRNUMBER = {3221548},
       DOI = {10.1007/978-3-0348-0405-9_19},
}

@article {dm-h-simplex,
    AUTHOR = {Dimakis, A. and M\"{u}ller-Hoissen, F.},
     TITLE = {Simplex and polygon equations},
   JOURNAL = {SIGMA Symmetry Integrability Geom. Methods Appl.},
  FJOURNAL = {SIGMA. Symmetry, Integrability and Geometry. Methods and Applications},
    VOLUME = {11},
      YEAR = {2015},
     PAGES = {Paper 042, 49},
   MRCLASS = {06A07 (16T25 52B12 82B23)},
  MRNUMBER = {3353831},
MRREVIEWER = {Joseph Kung},
       DOI = {10.3842/SIGMA.2015.042},
}

@Article{er,
  author     = {Edelman, P. H. and Reiner, V.},
  journal    = {Mathematika},
  title      = {The higher {S}tasheff--{T}amari posets},
  year       = {1996},
  number     = {1},
  pages      = {127--154},
  volume     = {43},
  doi        = {10.1112/S0025579300011633},
  fjournal   = {Mathematika. A Journal of Pure and Applied Mathematics},
  mrclass    = {52B05 (06A06 57Q15)},
  mrnumber   = {1401712},
  mrreviewer = {Margaret M. Bayer},
}

@Article{galashin,
  author   = {Galashin, P.},
  journal  = {Proc. Lond. Math. Soc. (3)},
  title    = {Plabic graphs and zonotopal tilings},
  year     = {2018},
  issn     = {0024-6115},
  number   = {4},
  pages    = {661--681},
  volume   = {117},
  doi      = {10.1112/plms.12139},
  fjournal = {Proceedings of the London Mathematical Society. Third Series},
  mrclass  = {52C22 (05B45 05E99)},
  mrnumber = {3873131},
}

@misc{gp,
	AUTHOR = {Galashin, P. and Postnikov, A.},
	EPRINT = {1708.01329},
	EPRINTTYPE = {arxiv},
	TITLE = {Purity and separation for oriented matroids},
	YEAR = {2017}
}

@Article{hs-char-poly,
  author     = {Hallam, J. and Sagan, B.},
  journal    = {J. Combin. Theory Ser. A},
  title      = {Factoring the characteristic polynomial of a lattice},
  year       = {2015},
  pages      = {39--63},
  volume     = {136},
  doi        = {10.1016/j.jcta.2015.06.006},
  fjournal   = {Journal of Combinatorial Theory. Series A},
  mrclass    = {06A07 (05B35 06B05)},
  mrnumber   = {3383266},
  mrreviewer = {Joseph Kung},
}

@incollection {kv-poly,
    AUTHOR = {Kapranov, M. M. and Voevodsky, V. A.},
     TITLE = {Combinatorial-geometric aspects of polycategory theory: pasting schemes and higher {B}ruhat orders (list of results)},
      NOTE = {International Category Theory Meeting (Bangor, 1989 and Cambridge, 1990)},
   JOURNAL = {Cahiers Topologie G\'{e}om. Diff\'{e}rentielle Cat\'{e}g.},
  FJOURNAL = {Cahiers de Topologie et G\'{e}om\'{e}trie Diff\'{e}rentielle Cat\'{e}goriques},
    VOLUME = {32},
      YEAR = {1991},
    NUMBER = {1},
     PAGES = {11--27},
      ISSN = {0008-0004},
   MRCLASS = {18D05 (52B30)},
  MRNUMBER = {1130400},
MRREVIEWER = {R. H. Street},
}

@incollection {ms,
    AUTHOR = {Manin, Y. I. and Schechtman, V. V.},
     TITLE = {Arrangements of hyperplanes, higher braid groups and higher
              {B}ruhat orders},
 BOOKTITLE = {Algebraic number theory},
    SERIES = {Adv. Stud. Pure Math.},
    VOLUME = {17},
     PAGES = {289--308},
 PUBLISHER = {Academic Press, Boston, MA},
      YEAR = {1989},
   MRCLASS = {32S40 (20F36 52B30)},
  MRNUMBER = {1097620},
MRREVIEWER = {P. Orlik},
       DOI = {10.2969/aspm/01710289},
}

@article{njw-jm, 
	title={The combinatorics of tensor products of higher {A}uslander algebras of type ${A}$}, 
	DOI={10.1017/S0017089520000361}, 
	journal={Glasgow Math. J.}, 
	fjournal={Glasgow Mathematical Journal},
	publisher={Cambridge University Press}, 
	author={McMahon, J. and Williams, N. J.}, 
	year={2020},
	note = {To appear}
}

@misc{njw-hst,
	AUTHOR = {Williams, N. J.},
	EPRINT = {2007.12664},
	EPRINTTYPE = {arxiv},
	TITLE = {New interpretations of the higher {S}tasheff--{T}amari orders},
	YEAR = {2020}
}

@Misc{njw-hbo,
  author     = {Williams, N. J.},
  title      = {The first higher {S}tasheff--{T}amari orders are quotients of the higher {B}ruhat orders},
  year       = {2020},
  eprint     = {2012.10371},
  eprinttype = {arxiv},
}

@Article{rambau,
  author     = {Rambau, J.},
  journal    = {Mathematika},
  title      = {Triangulations of cyclic polytopes and higher {B}ruhat orders},
  year       = {1997},
  number     = {1},
  pages      = {162--194},
  volume     = {44},
  doi        = {10.1112/S0025579300012055},
  fjournal   = {Mathematika. A Journal of Pure and Applied Mathematics},
  mrclass    = {52B70 (52B05 52B12 57Q15)},
  mrnumber   = {1464385},
  mrreviewer = {Jes\'{u}s A. De Loera},
}

@inproceedings {thomas-bst,
    AUTHOR = {Thomas, H.},
     TITLE = {Maps between higher {B}ruhat orders and higher {S}tasheff--{T}amari posets},
 BOOKTITLE = {Formal Power Series and Algebraic Combinatorics},
      YEAR = {2003},
      ORGANIZATION = {Link\"oping University, Sweden},
}

@Misc{olarte_santos,
  author     = {Olarte, J. A. and Santos, F.},
  title      = {Hypersimplicial subdivisions},
  year       = {2019},
  eprint     = {1906.05764},
  eprinttype = {arxiv},
}

@InCollection{rs-baues,
  author     = {Rambau, J. and Santos, F.},
  title      = {The generalized {B}aues problem for cyclic polytopes. {I}},
  year       = {2000},
  note       = {Combinatorics of polytopes},
  number     = {1},
  pages      = {65--83},
  volume     = {21},
  doi        = {10.1006/eujc.1999.0321},
  fjournal   = {European Journal of Combinatorics},
  issn       = {0195-6698},
  journal    = {European J. Combin.},
  mrclass    = {52B11 (52B12 52B70)},
  mrnumber   = {1737328},
  mrreviewer = {Jes\'{u}s A. De Loera},
}

@Comment{jabref-meta: databaseType:bibtex;}

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