@article {Bj-AIM1984,
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     TITLE = {Some combinatorial and algebraic properties of {C}oxeter
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   JOURNAL = {Adv. in Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {52},
      YEAR = {1984},
    NUMBER = {3},
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      ISSN = {0001-8708},
   MRCLASS = {52A25 (05B35 13H10 20G15)},
  MRNUMBER = {744856},
MRREVIEWER = {S. Milne},
       DOI = {10.1016/0001-8708(84)90021-5},
}

@article {BBLSSW1999, 
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     TITLE = {Complexes of not {$i$}-connected graphs},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {38},
      YEAR = {1999},
    NUMBER = {2},
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      ISSN = {0040-9383},
   MRCLASS = {57M15 (05C10 57M25)},
  MRNUMBER = {1660341},
MRREVIEWER = {Manoj K. Chari},
       DOI = {10.1016/S0040-9383(98)00009-3},
}

@article {BjWachsII1997,
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     TITLE = {Shellable nonpure complexes and posets. {II}},
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}
@article {BjWachsI1996,
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     TITLE = {Shellable nonpure complexes and posets. {I}},
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  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {348},
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  MRNUMBER = {1333388},
MRREVIEWER = {T. S. Blyth},
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}

@book {Golumbic1980,
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@incollection {Froberg1990,
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 BOOKTITLE = {Topics in algebra, {P}art 2 ({W}arsaw, 1988)},
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@article {BacEuJC1982,
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    VOLUME = {3},
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@article {DeshpandeSingh2021,
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     TITLE = {Higher independence complexes of graphs and their homotopy type},
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@article {JJMV2019,
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  FJOURNAL = {},
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@incollection {Forman2007,
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 BOOKTITLE = {Geometric combinatorics},
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   MRCLASS = {58E05 (05C99 05E99 52B70 57R70)},
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       DOI = {10.1090/pcms/013/04},
}
		
@article {Forman2002,
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   JOURNAL = {S\'{e}m. Lothar. Combin.},
  FJOURNAL = {S\'{e}minaire Lotharingien de Combinatoire},
    VOLUME = {48},
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     PAGES = {Art. B48c, 35},
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  MRNUMBER = {1939695},
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@article {Forman1998,
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@book {JonssonBook2008,
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 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2008},
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   MRCLASS = {05C10 (05C20 05C40 05E30 06A11 55U10)},
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@article {LinSharesh2003,
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       DOI = {10.1137/S0895480100366968},
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@article {kim-lew,
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   JOURNAL = {S\'{e}m. Lothar. Combin.},
  FJOURNAL = {S\'{e}minaire Lotharingien de Combinatoire},
    VOLUME = {84B},
      YEAR = {2020},
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   DOI = {10.1007/s11856-022-2308-4},
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@article {LinShareshWelker2008,
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     TITLE = {Complexes of graphs with bounded matching size},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {27},
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    NUMBER = {3},
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   MRCLASS = {05C70 (05A15 05C10)},
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       DOI = {10.1007/s10801-007-0092-1},
}

@book {RPSEC11997,
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      NOTE = {With a foreword by Gian-Carlo Rota,
              Corrected reprint of the 1986 original},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1997},
     PAGES = {xii+325},
      ISBN = {0-521-55309-1; 0-521-66351-2},
   MRCLASS = {05-02 (05A15 06-02 11-02)},
  MRNUMBER = {1442260},
MRREVIEWER = {Wayne M. Dymacek},
       DOI = {10.1017/CBO9780511805967},
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@book {RPSEC21999,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Enumerative combinatorics. {V}ol. 2},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {62},
      NOTE = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey
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 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1999},
     PAGES = {xii+581},
      ISBN = {0-521-56069-1; 0-521-78987-7},
   MRCLASS = {05A15 (05-02 05E05 05E10 68R05)},
  MRNUMBER = {1676282},
MRREVIEWER = {Ira Gessel},
       DOI = {10.1017/CBO9780511609589},
}

@article {RPSGaP1982,
    AUTHOR = {Stanley, Richard P.},
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    VOLUME = {32},
      YEAR = {1982},
    NUMBER = {2},
     PAGES = {132--161},
      ISSN = {0097-3165},
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  MRNUMBER = {654618},
MRREVIEWER = {R. J. Bumcrot},
       DOI = {10.1016/0097-3165(82)90017-6},
}

@book {RPSCCA1996,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Combinatorics and commutative algebra},
    SERIES = {Progress in Mathematics},
    VOLUME = {41},
   EDITION = {Second},
 PUBLISHER = {Birkh\"{a}user Boston Inc. Boston MA},
      YEAR = {1996},
     PAGES = {x+164},
      ISBN = {0-8176-3836-9},
   MRCLASS = {05-02 (13F50)},
  MRNUMBER = {1453579},
MRREVIEWER = {Volkmar Welker},
}

@incollection {WachsPosetTop2007,
    AUTHOR = {Wachs, Michelle L.},
     TITLE = {Poset topology: tools and applications},
 BOOKTITLE = {Geometric combinatorics},
    SERIES = {IAS/Park City Math. Ser.},
    VOLUME = {13},
     PAGES = {497--615},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2007},
   MRCLASS = {06B30 (05E10 52C35 55R80)},
  MRNUMBER = {2383132},
       DOI = {10.1090/pcms/013/09},
}

@article {QFibLemma1978,
    AUTHOR = {Quillen, Daniel},
     TITLE = {Homotopy properties of the poset of nontrivial {$p$}-subgroups
              of a group},
   JOURNAL = {Adv. in Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {28},
      YEAR = {1978},
    NUMBER = {2},
     PAGES = {101--128},
      ISSN = {0001-8708},
   MRCLASS = {20J99},
  MRNUMBER = {493916},
MRREVIEWER = {Kenneth S. Brown},
       DOI = {10.1016/0001-8708(78)90058-0},
}

@book {Koz2008, 
    AUTHOR = {Kozlov, Dmitry},
     TITLE = {Combinatorial algebraic topology},
    SERIES = {Algorithms and Computation in Mathematics},
    VOLUME = {21},
 PUBLISHER = {Springer, Berlin},
      YEAR = {2008},
     PAGES = {xx+389},
      ISBN = {978-3-540-71961-8},
   MRCLASS = {55-02 (05C15 05C25 06A07 52B70 55U10 57-02)},
  MRNUMBER = {2361455},
MRREVIEWER = {Rade \v{Z}ivaljevi\'{c}},
       DOI = {10.1007/978-3-540-71962-5},
}

@incollection {BjTopMeth1995,
    AUTHOR = {Bj\"{o}rner, A.},
     TITLE = {Topological methods},
 BOOKTITLE = {Handbook of combinatorics, {V}ol. 1, 2},
     PAGES = {1819--1872},
 PUBLISHER = {Elsevier Sci. B. V., Amsterdam},
      YEAR = {1995},
   MRCLASS = {52B05 (05B35 05E25 52B40)},
  MRNUMBER = {1373690},
MRREVIEWER = {Andrew Vince},
}


@article {MR2115080,
    AUTHOR = {Bj\"{o}rner, Anders and Wachs, Michelle L. and Welker, Volkmar},
     TITLE = {Poset fiber theorems},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {357},
      YEAR = {2005},
    NUMBER = {5},
     PAGES = {1877--1899},
      ISSN = {0002-9947},
   MRCLASS = {05E25 (06A11 55P10)},
  MRNUMBER = {2115080},
MRREVIEWER = {Edward B. Swartz},
       DOI = {10.1090/S0002-9947-04-03496-8},
}
		
@article {BjWachsTAMSII1996, 
    AUTHOR = {Bj\"{o}rner, Anders and Wachs, Michelle L.},
     TITLE = {Shellable nonpure complexes and posets. {II}},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {349},
      YEAR = {1997},
    NUMBER = {10},
     PAGES = {3945--3975},
      ISSN = {0002-9947},
   MRCLASS = {06A08 (05E99)},
  MRNUMBER = {1401765},
MRREVIEWER = {Volkmar Welker},
       DOI = {10.1090/S0002-9947-97-01838-2},
}
		

		
@article {MR946427,
    AUTHOR = {Bj\"{o}rner, Anders and Wachs, Michelle L.},
     TITLE = {Generalized quotients in {C}oxeter groups},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {308},
      YEAR = {1988},
    NUMBER = {1},
     PAGES = {1--37},
      ISSN = {0002-9947},
   MRCLASS = {05A99 (06F99 20B30 20F99)},
  MRNUMBER = {946427},
MRREVIEWER = {Joseph Kung},
       DOI = {10.2307/2000946},
}
		
@article {BjWachsTAMS1983, 
    AUTHOR = {Bj\"{o}rner, Anders and Wachs, Michelle},
     TITLE = {On lexicographically shellable posets},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {277},
      YEAR = {1983},
    NUMBER = {1},
     PAGES = {323--341},
      ISSN = {0002-9947},
   MRCLASS = {06A10 (05A99 52A25 57Q05)},
  MRNUMBER = {690055},
MRREVIEWER = {R. P. Dilworth},
       DOI = {10.2307/1999359},
}
		
@article {BjTAMS1980,  
    AUTHOR = {Bj\"{o}rner, Anders},
     TITLE = {Shellable and {C}ohen-{M}acaulay partially ordered sets},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {260},
      YEAR = {1980},
    NUMBER = {1},
     PAGES = {159--183},
      ISSN = {0002-9947},
   MRCLASS = {06A10 (13H10 52A25)},
  MRNUMBER = {570784},
MRREVIEWER = {P. McMullen},
       DOI = {10.2307/1999881},
}

@incollection {BjHCF1998, 
    AUTHOR = {Bj\"{o}rner, Anders},
     TITLE = {A general homotopy complementation formula},
      NOTE = {Selected papers in honor of Adriano Garsia (Taormina, 1994)},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {193},
      YEAR = {1998},
    NUMBER = {1-3},
     PAGES = {85--91},
      ISSN = {0012-365X},
   MRCLASS = {06A07 (55P15)},
  MRNUMBER = {1661364},
MRREVIEWER = {Laura M. Anderson},
       DOI = {10.1016/S0012-365X(98)00136-8},
}

@article {BJWalkerHCF1983,  
    AUTHOR = {Bj\"{o}rner, Anders and Walker, James W.},
     TITLE = {A homotopy complementation formula for partially ordered sets},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {4},
      YEAR = {1983},
    NUMBER = {1},
     PAGES = {11--19},
      ISSN = {0195-6698},
   MRCLASS = {06A10 (05A15 06C10 55P99)},
  MRNUMBER = {694463},
MRREVIEWER = {Hartmut H\"{o}ft},
       DOI = {10.1016/S0195-6698(83)80003-1},
}

@article {BjJCTA1981,  
    AUTHOR = {Bj\"{o}rner, Anders},
     TITLE = {Homotopy type of posets and lattice complementation},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {30},
      YEAR = {1981},
    NUMBER = {1},
     PAGES = {90--100},
      ISSN = {0097-3165},
   MRCLASS = {06A10 (06B99 18G99 55P99)},
  MRNUMBER = {607041},
       DOI = {10.1016/0097-3165(81)90042-X},
}

@article {BjEuJC1984,
    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},
      ISSN = {0195-6698},
   MRCLASS = {06A10 (52A25 57Q05)},
  MRNUMBER = {746039},
MRREVIEWER = {Udo Pachner},
       DOI = {10.1016/S0195-6698(84)80012-8},
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@article {MR1816254,
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   JOURNAL = {J. Combin. Theory Ser. A},
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    VOLUME = {94},
      YEAR = {2001},
    NUMBER = {1},
     PAGES = {156--168},
      ISSN = {0097-3165},
   MRCLASS = {05E25 (20C30)},
  MRNUMBER = {1816254},
       DOI = {10.1006/jcta.2000.3128},
}

@article {TopTwoJAPA2001,  
    AUTHOR = {Sundaram, Sheila},
     TITLE = {On the topology of two partition posets with forbidden block
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   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {155},
      YEAR = {2001},
    NUMBER = {2-3},
     PAGES = {271--304},
      ISSN = {0022-4049},
   MRCLASS = {06A11 (06B30 20C30 55P99)},
  MRNUMBER = {1801419},
MRREVIEWER = {Joseph Neggers},
       DOI = {10.1016/S0022-4049(99)00090-0},
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@article {NonmodJAC1999, 
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     TITLE = {Homotopy of non-modular partitions and the {W}hitehouse
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   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
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      YEAR = {1999},
    NUMBER = {3},
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      ISSN = {0925-9899},
   MRCLASS = {05E25 (06A11 20C30)},
  MRNUMBER = {1695076},
MRREVIEWER = {Eva-Maria E. Feichtner},
       DOI = {10.1023/A:1018648219348},
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@article {SuAIM1994,
    AUTHOR = {Sundaram, Sheila},
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   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
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      YEAR = {1994},
    NUMBER = {2},
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   MRCLASS = {05E25 (20C30)},
  MRNUMBER = {1273390},
       DOI = {10.1006/aima.1994.1030},
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@incollection {Jer93,
    AUTHOR = {Sundaram, Sheila},
     TITLE = {Applications of the {H}opf trace formula to computing homology
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 BOOKTITLE = {Jerusalem combinatorics '93},
    SERIES = {Contemp. Math.},
    VOLUME = {178},
     PAGES = {277--309},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1994},
   MRCLASS = {05E25 (20C30)},
  MRNUMBER = {1310588},
MRREVIEWER = {C. S. Hoo},
       DOI = {10.1090/conm/178/01904},
}
		
@article {WelkerJCTA1995,
    AUTHOR = {Welker, Volkmar},
     TITLE = {Equivariant homotopy of posets and some applications to
              subgroup lattices},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {69},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {61--86},
      ISSN = {0097-3165},
   MRCLASS = {05E25 (20D30)},
  MRNUMBER = {1309152},
MRREVIEWER = {Jacques Th\'{e}venaz},
       DOI = {10.1016/0097-3165(95)90107-8},
}
@article {SolJAlg1968,
    AUTHOR = {Solomon, Louis},
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   JOURNAL = {J. Algebra},
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    VOLUME = {9},
      YEAR = {1968},
     PAGES = {220--239},
      ISSN = {0021-8693},
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  MRNUMBER = {232868},
MRREVIEWER = {T. Ono},
       DOI = {10.1016/0021-8693(68)90022-7},
}

@book {Hatcher2002,
    AUTHOR = {Hatcher, Allen},
     TITLE = {Algebraic topology},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2002},
     PAGES = {xii+544},
      ISBN = {0-521-79160-X; 0-521-79540-0},
   MRCLASS = {55-01 (55-00)},
  MRNUMBER = {1867354},
MRREVIEWER = {Donald W. Kahn},
}

@book {WestGraphTheory1996,
    AUTHOR = {West, Douglas B.},
     TITLE = {Introduction to graph theory},
 PUBLISHER = {Prentice Hall Inc. Upper Saddle River NJ},
      YEAR = {1996},
     PAGES = {xvi+512},
      ISBN = {0-13-227828-6},
   MRCLASS = {05-01},
  MRNUMBER = {1367739},
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@article {provan-billera,
    AUTHOR = {Provan, J. Scott and Billera, Louis J.},
     TITLE = {Decompositions of simplicial complexes related to diameters of
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@book {hough,
    AUTHOR = {Hough,~Wesley~Kyle},
     TITLE = {On~{I}ndependence,~{M}atching,~and~{H}omomorphism~{C}omplexes},
      NOTE = {Thesis (Ph.D.)--University of Kentucky},
 PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
      YEAR = {2017},
     PAGES = {57},
      ISBN = {978-1369-98951-9},
   MRCLASS = {Thesis},
  MRNUMBER = {3698933},
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@article {BDJRSX,
    AUTHOR = {Bayer, Margaret and Denker, Mark and Jeli\'c Milutinovi\'c, Marija and Rowlands, Rowan and  Sundaram, Sheila and Xue, Lei},
     TITLE = {Topology of cut complexes of graphs},
   JOURNAL = {},
   NOTE = {in preparation},
  FJOURNAL = {},
    VOLUME = {},
      YEAR = {2023},
    NUMBER = {},
     PAGES = {},
      ISSN = {},
   MRCLASS = {},
  MRNUMBER = {},
MRREVIEWER = {},
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}

@article {BDJRSX-TOTAL2022,
    AUTHOR = {Bayer, Margaret and Denker, Mark and Jeli\'c Milutinovi\'c, Marija and Rowlands, Rowan and  Sundaram, Sheila and Xue, Lei},
     TITLE = {Total cut complexes of graphs},
   JOURNAL = {arXiv.2209.13503},
   NOTE = {},
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    VOLUME = {},
      YEAR = {2022},
    NUMBER = {},
     PAGES = {},
      ISSN = {},
   MRCLASS = {},
  MRNUMBER = {},
MRREVIEWER = {},
       DOI = {10.48550/ARXIV.2209.13503 },
}

@misc{https://doi.org/10.48550/arxiv.2106.10863,
  doi = {10.48550/ARXIV.2106.10863},
  url = {https://arxiv.org/abs/2106.10863},
  author = {Abdelmalek, Fred M. and Deshpande, Priyavrat and Goyal, Shuchita and Roy, Amit and Singh, Anurag},
  keywords = {Combinatorics (math.CO), Commutative Algebra (math.AC), FOS: Mathematics, FOS: Mathematics, (2010) class: 05E45, 13F55},
  title = {Chordal graphs, higher independence and vertex decomposable complexes},
  publisher = {arXiv},
  year = {2021},
  copyright = {Creative Commons Attribution 4.0 International},
}

@book {VINK2008,
    AUTHOR = {Viro, O. Ya. and Ivanov, O. A. and Netsvetaev, N. Yu. and
              Kharlamov, V. M.},
     TITLE = {Elementary topology},
      NOTE = {Problem textbook},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2008},
     PAGES = {xx+400},
      ISBN = {978-0-8218-4506-6},
   MRCLASS = {55-01 (54-01 57-01)},
  MRNUMBER = {2444949},
MRREVIEWER = {Leonard R. Rubin},
       DOI = {10.1090/mbk/054},
}


@book {LeeITM2011,
    AUTHOR = {Lee, John M.},
     TITLE = {Introduction to topological manifolds},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {202},
   EDITION = {Second},
 PUBLISHER = {Springer, New York},
      YEAR = {2011},
     PAGES = {xviii+433},
      ISBN = {978-1-4419-7939-1},
   MRCLASS = {57-01 (54-01 55-01)},
  MRNUMBER = {2766102},
       DOI = {10.1007/978-1-4419-7940-7},
}

@book {Matousek2003,
    AUTHOR = {Matou\v{s}ek, Ji\v{r}\'{\i}},
     TITLE = {Using the {B}orsuk-{U}lam theorem},
    SERIES = {Universitext},
      NOTE = {Lectures on topological methods in combinatorics and geometry,
              Written in cooperation with Anders Bj\"{o}rner and G\"{u}nter M.
              Ziegler},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2003},
     PAGES = {xii+196},
      ISBN = {3-540-00362-2},
   MRCLASS = {55-01 (05-01 52-01 52A35 55M20)},
  MRNUMBER = {1988723},
MRREVIEWER = {Zdzis\l aw Dzedzej},
}