% This is an example bibliography file for FPSAC submissions.

@article{greenwade93,
  author        = {George D. Greenwade},
  date-modified = {2016-08-11 21:04:25 +0000},
  journal       = {TUGBoat},
  number        = {3},
  pages         = {342--351},
  title         = {The {C}omprehensive {T}ex {A}rchive {N}etwork ({CTAN})},
  url           = {https://www.google.com},
  volume        = {14},
  year          = {1993},
  bdsk-url-1    = {https://www.google.com}
}

@article{MR4,
  author     = {Corliss, J. J.},
  title      = {Upper limits to the real roots of a real algebraic equation},
  journal    = {Amer. Math. Monthly},
  fjournal   = {The American Mathematical Monthly},
  volume     = {46},
  year       = {1939},
  pages      = {334--338},
  issn       = {0002-9890},
  mrclass    = {09.0X},
  mrnumber   = {0000004},
  mrreviewer = {O. Sz\'asz},
  doi        = {10.2307/2302887}
}

@book{anderson2023equivariant,
    AUTHOR = {Anderson, David and Fulton, William},
     TITLE = {Equivariant cohomology in algebraic geometry},
    SERIES = {Cambridge Stud. Adv. Math.},
    VOLUME = {210},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2024},
     PAGES = {xv+446 pp.}, 
       DOI = {10.1017/9781009349994}
}

@article {monk,
    AUTHOR = {Monk, D.},
     TITLE = {The geometry of flag manifolds},
   JOURNAL = {Proc. London Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {9},
      YEAR = {1959},
     PAGES = {253--286},
   MRCLASS = {14.00 (50.00)},
  MRNUMBER = {106911},
MRREVIEWER = {W.\ Burau},
       DOI = {10.1112/plms/s3-9.2.253},
}

@article {sottile-pieri,
    AUTHOR = {Sottile, F.},
     TITLE = {Pieri's formula for flag manifolds and {S}chubert polynomials},
   JOURNAL = {Ann. Inst. Fourier (Grenoble)},
  FJOURNAL = {Universit\'{e} de Grenoble. Annales de l'Institut Fourier},
    VOLUME = {46},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {89--110},
   MRCLASS = {14M15 (05E05 05E15)},
  MRNUMBER = {1385512},
MRREVIEWER = {Paolo\ Aluffi},
       URL = {http://www.numdam.org/item?id=AIF_1996__46_1_89_0},
}

@misc{knutson-separated-descent-puzzles,
      AUTHOR = {Knutson, A. and Zinn-Justin, P.},
      EPRINT = {2306.13855},
  EPRINTTYPE = {arxiv},
       TITLE = {Schubert puzzles and integrability III: separated descents},
        YEAR = {2023}}

@article {huang-separated-descent,
    AUTHOR = {Huang, D.},
     TITLE = {Schubert products for permutations with separated descents},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2023},
    NUMBER = {20},
     PAGES = {17461--17493},
   MRCLASS = {05E14 (05E05 14N15)},
  MRNUMBER = {4659856},
       DOI = {10.1093/imrn/rnac299},
}

@article {knutson-tao-puzzles,
    AUTHOR = {Knutson, A. and Tao, T.},
     TITLE = {Puzzles and (equivariant) cohomology of {G}rassmannians},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {119},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {221--260},
   MRCLASS = {14N15 (05E05 05E10 57R91 57S25)},
  MRNUMBER = {1997946},
       DOI = {10.1215/S0012-7094-03-11922-5},
}

@article {knutson-tao-woodward-puzzles,
    AUTHOR = {Knutson, A. and Tao, T. and Woodward, C.},
     TITLE = {The honeycomb model of {${\rm GL}_n(\mathbb{C})$} tensor products.
              {II}. {P}uzzles determine facets of the
              {L}ittlewood-{R}ichardson cone},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {17},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {19--48},
   MRCLASS = {14N15 (05E10 15A69 52B12)},
  MRNUMBER = {2015329},
MRREVIEWER = {Anders\ Skovsted\ Buch},
       DOI = {10.1090/S0894-0347-03-00441-7},
}

@article {buch-kresch-purbhoo-tamvakis-puzzle,
    AUTHOR = {Buch, A. S. and Kresch, A. and Purbhoo, K.
              and Tamvakis, H.},
     TITLE = {The puzzle conjecture for the cohomology of two-step flag
              manifolds},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {44},
      YEAR = {2016},
    NUMBER = {4},
     PAGES = {973--1007},
   MRCLASS = {05E05 (14M15 14N15 14N35)},
  MRNUMBER = {3566227},
MRREVIEWER = {Frank\ Sottile},
       DOI = {10.1007/s10801-016-0697-3},
}

@article {buch-kresch-tamvakis-GW,
    AUTHOR = {Buch, A. S. and Kresch, A. and Tamvakis, H.},
     TITLE = {Gromov-{W}itten invariants on {G}rassmannians},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {16},
      YEAR = {2003},
    NUMBER = {4},
     PAGES = {901--915},
   MRCLASS = {14N35 (14M15)},
  MRNUMBER = {1992829},
MRREVIEWER = {Andreas\ Gathmann},
       DOI = {10.1090/S0894-0347-03-00429-6},
}

@misc{knutson-zinn-justin-puzzle1,
      AUTHOR = {Knutson, A. and Zinn-Justin, P.},
      EPRINT = {1706.10019},
  EPRINTTYPE = {arxiv},
       TITLE = {Schubert puzzles and integrability I: invariant trilinear forms},
        YEAR = {2017}}

@article {karupp-boolean,
    AUTHOR = {Karuppuchamy, P.},
     TITLE = {On {S}chubert varieties},
   JOURNAL = {Comm. Algebra},
  FJOURNAL = {Communications in Algebra},
    VOLUME = {41},
      YEAR = {2013},
    NUMBER = {4},
     PAGES = {1365--1368},
   MRCLASS = {14M15 (14M25)},
  MRNUMBER = {3044412},
MRREVIEWER = {Harry\ Tamvakis},
       DOI = {10.1080/00927872.2011.635620},
}

@article {levi-spherical-2,
    AUTHOR = {Gao, Y. and Hodges, R. and Yong, A.},
     TITLE = {Levi-spherical {S}chubert varieties},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {439},
      YEAR = {2024},
     PAGES = {Paper No. 109486, 14 pp.},
   MRCLASS = {14M15 (20G05 20G07)},
  MRNUMBER = {4690502},
       DOI = {10.1016/j.aim.2024.109486},
}
@article {levi-spherical-1,
    AUTHOR = {Gao, Y. and Hodges, R. and Yong, A.},
     TITLE = {Classification of {L}evi-spherical {S}chubert varieties},
   JOURNAL = {Selecta Math. (N.S.)},
  FJOURNAL = {Selecta Mathematica. New Series},
    VOLUME = {29},
      YEAR = {2023},
    NUMBER = {4},
     PAGES = {Paper No. 55, 40 pp.},
   MRCLASS = {14M27 (05E10 05E14)},
  MRNUMBER = {4615612},
MRREVIEWER = {Hiro-Fumi\ Yamada},
       DOI = {10.1007/s00029-023-00856-9},
}

@article {tenner-boolean,
    AUTHOR = {Tenner, B. E.},
     TITLE = {Pattern avoidance and the {B}ruhat order},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {114},
      YEAR = {2007},
    NUMBER = {5},
     PAGES = {888--905},
   MRCLASS = {05E15 (06A07 20F55)},
  MRNUMBER = {2333139},
MRREVIEWER = {Alessandro\ Conflitti},
       DOI = {10.1016/j.jcta.2006.10.003},
}

@book {Bjorner-Brenti,
    AUTHOR = {Bj\"{o}rner, A. and Brenti, F.},
     TITLE = {Combinatorics of {C}oxeter groups},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {231},
 PUBLISHER = {Springer, New York},
      YEAR = {2005},
     PAGES = {xiv+363 pp.},
    DOI = {10.1007/3-540-27596-7} 
}

@misc{gao2020boolean,
      AUTHOR = {Gao, Y. and H{\"a}nni, K.},
      EPRINT = {2007.08490},
  EPRINTTYPE = {arxiv},
       TITLE = {Boolean elements in the Bruhat order},
        YEAR = {2020}}

@article {postnikov-FK,
    AUTHOR = {M\'{e}sz\'{a}ros, K. and Panova, G. and Postnikov,
              A.},
     TITLE = {Schur times {S}chubert via the {F}omin-{K}irillov algebra},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {21},
      YEAR = {2014},
    NUMBER = {1},
     PAGES = {Paper 1.39, 22 pp.},
   MRCLASS = {05E05 (14N35)},
  MRNUMBER = {3177534},
MRREVIEWER = {Shengmao\ Zhu},
       DOI = {10.37236/3659},
}

@article {lenart-sottile-skew-Schubert,
    AUTHOR = {Lenart, C. and Sottile, F.},
     TITLE = {Skew {S}chubert polynomials},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {131},
      YEAR = {2003},
    NUMBER = {11},
     PAGES = {3319--3328},
   MRCLASS = {05E15 (06A07 14M15)},
  MRNUMBER = {1990619},
MRREVIEWER = {Mikhail\ Kogan},
       DOI = {10.1090/S0002-9939-03-06919-3},
}

@article {lenart-growth-diagram,
    AUTHOR = {Lenart, C.},
     TITLE = {Growth diagrams for the {S}chubert multiplication},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {117},
      YEAR = {2010},
    NUMBER = {7},
     PAGES = {842--856},
   MRCLASS = {05E05 (14M15)},
  MRNUMBER = {2652098},
MRREVIEWER = {Edward\ E.\ Allen},
       DOI = {10.1016/j.jcta.2010.02.004},
}

@incollection {robichaux-survey,
    AUTHOR = {Robichaux, C. and Yadav, H. and Yong, A.},
     TITLE = {Equivariant cohomology, {S}chubert calculus, and edge labeled
              tableaux},
 BOOKTITLE = {Facets of algebraic geometry. {V}ol. {II}},
    SERIES = {London Math. Soc. Lecture Note Ser.},
    VOLUME = {473},
     PAGES = {284--335},
 PUBLISHER = {Cambridge Univ. Press, Cambridge},
      YEAR = {2022},
   MRCLASS = {05E14 (14M15 14N15)},
  MRNUMBER = {4381918},
}

@article{kostant1986nil,
    AUTHOR = {Kostant, Bertram and Kumar, Shrawan},
     TITLE = {The nil {H}ecke ring and cohomology of {$G/P$} for a
              {K}ac-{M}oody group {$G$}},
   JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
  FJOURNAL = {Proceedings of the National Academy of Sciences of the United
              States of America},
    VOLUME = {83},
      YEAR = {1986},
    NUMBER = {6},
     PAGES = {1543--1545}, 
       DOI = {10.1073/pnas.83.6.1543}, 
}

@misc{richmond2023nil,
      AUTHOR = {Richmond, E. and Zainoulline, K.},
      EPRINT = {2310.01167},
  EPRINTTYPE = {arxiv},
       TITLE = {{N}il-{H}ecke rings and the {S}chubert calculus},
        YEAR = {2023}}

@book{kumar2012kac,
    AUTHOR = {Kumar, Shrawan},
     TITLE = {Kac-{M}oody groups, their flag varieties and representation
              theory},
    SERIES = {Progr. Math.},
    VOLUME = {204},
 PUBLISHER = {Birkh\"auser Boston, Inc.},
      YEAR = {2002},
     PAGES = {xvi+606 pp.},
       DOI = {10.1007/978-1-4612-0105-2}, 
}