% This is an example bibliography file for FPSAC submissions.

@book {bourbaki1968,
    AUTHOR = {Bourbaki, Nicolas},
     TITLE = {Lie {G}roups and {L}ie {A}lgebras. {C}hapters 4--6},
    SERIES = {Elements of Mathematics (Berlin)},
      NOTE = {Translated from the 1968 French original by Andrew Pressley},
 PUBLISHER = {Springer-Verlag},
   address = {Berlin},
      YEAR = {2002},
     PAGES = {xii+300}}

@article {bjorner2009shape,
    AUTHOR = {Bj\"{o}rner, Anders and Ekedahl, Torsten},
     TITLE = {On the shape of {B}ruhat intervals},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {170},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {799--817}}

@unpublished{braden2020singular,
    author = {Braden, Tom and Huh, June and Matherne, Jacob P and Proudfoot, Nicholas and Wang, Botong},
    title = {Singular Hodge theory for combinatorial geometries},
    eprint = {2010.06088},
    year = {2020}}

@unpublished{brentisome,
  title={Some open problems on Coxeter groups and unimodality},
  author={Brenti, Francesco},
  note = {Available at \url{https://www.samuelfhopkins.com/OPAC/files/proceedings/brenti.pdf}},
  year = {2022}}

@unpublished{castillo2023size,
    author = {Castillo, Federico and de la Fuente, Damian and Libedinsky, Nicolas and Plaza, David},
    title = {On the size of Bruhat intervals},
    eprint = {2309.08539},
    year={2023}}

@article {duistermaat1982variation,
    AUTHOR = {Duistermaat, Johannes J. and Heckman, Gerrit J.},
     TITLE = {On the variation in the cohomology of the symplectic form of
              the reduced phase space},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {69},
      YEAR = {1982},
    NUMBER = {2},
     PAGES = {259--268}}

@article {elias2014hodge,
    AUTHOR = {Elias, Ben and Williamson, Geordie},
     TITLE = {The {H}odge theory of {S}oergel bimodules},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {180},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {1089--1136}}

@article {graham1996logarithmic,
    AUTHOR = {Graham, William},
     TITLE = {Logarithmic convexity of push-forward measures},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {123},
      YEAR = {1996},
    NUMBER = {2},
     PAGES = {315--322}}

@article {heckman1982projections,
    AUTHOR = {Heckman, Gerrit J.},
     TITLE = {Projections of orbits and asymptotic behavior of
              multiplicities for compact connected {L}ie groups},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {67},
      YEAR = {1982},
    NUMBER = {2},
     PAGES = {333--356}}

@article {huh2017enumeration,
    AUTHOR = {Huh, June and Wang, Botong},
     TITLE = {Enumeration of points, lines, planes, etc.},
   JOURNAL = {Acta Math.},
  FJOURNAL = {Acta Mathematica},
    VOLUME = {218},
      YEAR = {2017},
    NUMBER = {2},
     PAGES = {297--317}}

@unpublished{melvin2020soergel,
    author = {Melvin, George and Slofstra, William},
    title = {Soergel bimodules and the shape of Bruhat intervals},
    note = {preprint, available at \url{https://math.berkeley.edu/~gmelvin/bruhatshape.pdf}},
   YEAR = {2020},
}

@article {okounkov1996brunn,
    AUTHOR = {Okounkov, Andrei},
     TITLE = {Brunn-{M}inkowski inequality for multiplicities},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {125},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {405--411}}

@article{okounkov1997log,
AUTHOR = {Okounkov, Andrei},
     TITLE = {Log-concavity of multiplicities with application to characters of $U(\infty)$},
JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
   VOLUME = {127},
   YEAR = {1997},
   NUMBER = {2},
 PAGES = {258--282}
}

@article{patimo2022singular,
 AUTHOR = {Patimo, Leonardo},
  TITLE = {Singular Rouquier complexes},
JOURNAL = {Proc. Lond. Math. Soc.},
FJOURNAL = {Proceedings of the London Mathematical Society},
   VOLUME = {125},
 YEAR = {2002},
   NUMBER = {6},
 PAGES = {1332--1352}
}

@article {stanton1990unimodality,
    AUTHOR = {Stanton, Dennis},
     TITLE = {Unimodality and {Y}oung's lattice},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {54},
      YEAR = {1990},
    NUMBER = {1},
     PAGES = {41--53}}

@unpublished{BGHpolytope,
    author = {Burrull, Gaston and Gui, Tao and Hu, Hongsheng},
    title = {On the dominant weight polytopes},
    eprint = {2311.16022},
    year = {2023}}

@unpublished{BGHlogconcave,
    author = {Burrull, Gaston and Gui, Tao and Hu, Hongsheng},
    title = {Asymptotic log-concavity of dominant lower {B}ruhat intervals via {B}runn--{M}inkowski inequality},
    eprint = {2311.17980},
   year = {2024}}

@article{ehrhart1962polyedres,
  title={Sur les poly{\`e}dres rationnels homoth{\'e}tiques {\`a} n dimensions},
  author={Ehrhart, Eugene},
  journal={CR Acad. Sci. Paris},
  volume={254},
  pages={616},
  year={1962}
}

@misc{BLV,
      title={On the classification of {B}ruhat intervals}, 
      author={Burrull, Gaston and Libedinsky, Nicolas and Villegas Rodrigo},
      note={Work in progress},
}

@misc{stacks,
    author       = {The {Stacks Project Authors}},
    title        = {The {S}tacks {P}roject},
    howpublished = {\url{https://stacks.math.columbia.edu/tag/0BJ8}}}