@article {Mészáros_Morales_2018,
    AUTHOR = {M\'{e}sz\'{a}ros, K. and Morales, A. H.},
     TITLE = {Volumes and {E}hrhart polynomials of flow polytopes},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {293},
      YEAR = {2019},
    NUMBER = {3-4},
     PAGES = {1369--1401},
      ISSN = {0025-5874},
   MRCLASS = {52B20 (05C90)},
  MRNUMBER = {4024590},
       DOI = {10.1007/s00209-019-02283-z},
       URL = {https://doi.org/10.1007/s00209-019-02283-z},
}
 
 
 @article {Pitman_Stanley_1999,
    AUTHOR = {Stanley, R. P. and Pitman, J.},
     TITLE = {A polytope related to empirical distributions, plane trees,
              parking functions, and the associahedron},
   JOURNAL = {Discrete Comput. Geom.},
    VOLUME = {27},
      YEAR = {2002},
    NUMBER = {4},
     PAGES = {603--634}
}
 

@article{Baldoni_Vergne_2008,
  title={Kostant partitions functions and flow polytopes},
  author={Baldoni, W. and Vergne, M.},
  journal={Transform. Groups},
  volume={13},
  number={3-4},
  pages={447--469},
  year={2008},
  publisher={Springer}
}


 @article{Kreweras_1965, title={Sur une classe de problèmes de dénombrement liés au treillis des partitions des entiers}, url={https://www.semanticscholar.org/paper/Sur-une-classe-de-probl\%C3\%A8mes-de-d\%C3\%A9nombrement-li\%C3\%A9s-au-Kreweras/fcd13c9ee4d3f80fe48757137f5704f378b74539}, abstractNote={ion faite du facteur constant que l'on a sorti du signe !L dans la ligne (74), la somme Sh fait donc intervenir D = £ ( l ) b " k ( b ^ k ) R(a + k), qui n'est autre que la différence b-ième, pour t = a, de R(t). Pour que le lemme s'applique, il importe de s'assurer que a et b sont bien des entiers positifs satisfaisant à a < b. Or a est bien positif puisque a = h 1 et que l'on a pris h ^ 2 ; d'autre part h a été pris au plus égal à a, donc a = h 1 < a, et comme on a supposé a b, on a bien a < b. Le lemme 3.2.8. s'applique donc, et permet d'affirmer que D = 0, donc Sh = 0. Les sommes partielles Sh étant en fin de compte toutes nulles , le calcul fait à partir de la formule (73) établit bien que Pa'.b(b 1) = 0. Les propriétés (i) (ii) et (iii) des polynômes b(z) étant ainsi vérifiées, il en résulte, comme on l'a fait remarquer à la fin du §3.2.6, que ces polynômes sont bien identiques aux polynômes P a ? b(z) introduits au §3.2.3. Il s'ensuit finalement que la formule (66), qui avait été établie en définissant cp(h, k) par Ph k ( h k), est encore vraie si l'on définit cp(h, k) à l'aide de la formule (6 7), complétée par 9(0, 0) = 1, cp(l , 0) = cp(0, 1) = 1.}, journal={undefined}, author={Kreweras, G.}, year={1965} }


 @article{Computing_the_continuous_discretely_2007, volume={45}, ISSN={0009-4978, 1523-8253}, DOI={10.5860/CHOICE.45-0923}, number={02}, journal={Choice Reviews Online}, year={2007}, month={10}, pages={45-0923-45–0923} }
 
@article{Hille_2003,
title = {Quivers, cones and polytopes},
journal = {Linear Algebra and its Applications},
volume = {365},
pages = {215-237},
year = {2003},
note = {Special Issue on Linear Algebra Methods in Representation Theory},
issn = {0024-3795},
doi = {https://doi.org/10.1016/S0024-3795(02)00406-8},
url = {https://www.sciencedirect.com/science/article/pii/S0024379502004068},
author = {Lutz Hille},
keywords = {Quivers, Reflexive polytopes, Toric geometry},
abstract = {Let Q be a quiver without oriented cycles. We consider the polytope of flows Δ(ξ) in Q with input ξ. These polytopes are closely related to the combinatorial structure of the quiver, in particular, to its spanning subtrees. Furthermore, we consider a system of cones which turns out to be a fan and can be seen as a base for the family of all flow polytopes Δ(ξ) for the various inputs ξ. Finally, we present several examples.}
}

@misc{PSvolume,
title={Pitman--Stanley flow polytopes: volume and lattice points},
author={W. T. Dugan and M. Hegarty and A. H. Morales and A. Raymond},
note={In preparation}}

@misc{PSfaces,
title={Pitman--Stanley flow polytopes: vertices and faces},
author={W. T. Dugan and M. Hegarty and  A. H. Morales and  A. Raymond},
note={In preparation}}


@book {EC1,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Enumerative combinatorics. {V}olume 1},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {49},
   EDITION = {Second},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2012},
     PAGES = {xiv+626},
      ISBN = {978-1-107-60262-5}
}

@book {BS,
    AUTHOR = {Sagan, Bruce E.},
     TITLE = {The symmetric group},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {203},
   EDITION = {Second},
      NOTE = {Representations, combinatorial algorithms, and symmetric
              functions},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {2001},
     PAGES = {xvi+238},
      ISBN = {0-387-95067-2}
}


@online{oeis,
	organization = {OEIS Foundation Inc.},
	label = {OEIS},
	url = {http://oeis.org},
	title = {{The On-Line Encyclopedia of Integer Sequences}}
	}

@article{AP,
    author = {Postnikov, A.},
    title = "{Permutohedra, Associahedra, and Beyond}",
    journal = {International Mathematics Research Notices},
    volume = {2009},
    number = {6},
    pages = {1026-1106},
    year = {2009},
    month = {01}
}

@article {LMStD1,
    AUTHOR = {Liu, Ricky I. and M\'{e}sz\'{a}ros, Karola and St. Dizier, Avery},
     TITLE = {Gelfand-{T}setlin polytopes: a story of flow and order
              polytopes},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {33},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {2394--2415},
      ISSN = {0895-4801},
   MRCLASS = {05E10},
  MRNUMBER = {4039518},
MRREVIEWER = {Robert Davis},
       DOI = {10.1137/19M1251242},
       URL = {https://doi.org/10.1137/19M1251242},
}


@article{LMStD2,
  title={Schubert polynomials as projections of {M}inkowski sums of {G}elfand-{T}setlin polytopes},
    AUTHOR = {Liu, Ricky I. and M\'{e}sz\'{a}ros, Karola and St. Dizier, Avery},
  journal={Combin. Theory},
  year={2022},
  volume={2},
  number = {3}
}


@article {GalloSodini,
    AUTHOR = {Gallo, G. and Sodini, C.},
     TITLE = {Extreme points and adjacency relationship in the flow
              polytope},
   JOURNAL = {Calcolo},
  FJOURNAL = {Calcolo. A Quarterly on Numerical Analysis and Theory of
              Computation},
    VOLUME = {15},
      YEAR = {1978},
    NUMBER = {3},
     PAGES = {277--288},
      ISSN = {0008-0624},
   MRCLASS = {90B10 (90C25)},
  MRNUMBER = {555751},
MRREVIEWER = {Kailash C. Kapur},
       DOI = {10.1007/BF02575918},
       URL = {https://doi.org/10.1007/BF02575918},
}

@book {EC2,
    AUTHOR = {Stanley, Richard P.},
    TITLE = {Enumerative combinatorics. {V}ol. 2},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {62},
PUBLISHER = {Cambridge University Press, Cambridge},
     YEAR = {1999},
    PAGES = {xii+581},
}


@article {Caracol,
    AUTHOR = {Benedetti, C. and Gonz\'{a}lez D'Le\'{o}n, R. S. and Hanusa,
              C. R. H. and Harris, P. E. and Khare, A. and
              Morales, A. H. and Yip, M.},
     TITLE = {A combinatorial model for computing volumes of flow polytopes},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {372},
      YEAR = {2019},
    NUMBER = {5},
     PAGES = {3369--3404},
      ISSN = {0002-9947},
   MRCLASS = {05A15 (05A19 05C20 05C21 52A38 52B05 52B11)},
  MRNUMBER = {3988614},
MRREVIEWER = {Ruriko Yoshida},
       DOI = {10.1090/tran/7743},
       URL = {https://doi.org/10.1090/tran/7743},
}