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@book{triangulations,
	Author = {De Loera, J.-A. and Rambau, J. and Santos, F.},
	Date-Modified = {2019-05-28 17:49:15 +1000},
	Edition = {1},
	Isbn = {3642129706, 9783642129704},
	Publisher = {Springer},
	Title = {Triangulations: Structures for Algorithms and Applications},
	Year = {2010}}

@book{BB05,
	Author = {Bj\"{o}rner, Anders and Brenti, Francesco},
	Isbn = {978-3540-442387; 3-540-44238-3},
	Mrclass = {05-01 (05E15 20F55)},
	Mrnumber = {2133266},
	Mrreviewer = {Jian-yi Shi},
	Pages = {xiv+363},
	Publisher = {Springer, New York},
	Series = {Graduate Texts in Mathematics},
	Title = {Combinatorics of {C}oxeter groups},
	Volume = {231},
	Year = {2005}}

@article{HLT,
	Author = {Hohlweg, C. and Lange, C. and Thomas, H.},
	Date-Modified = {2019-05-28 17:51:52 +1000},
	Doi = {10.1016/j.aim.2010.07.005},
	Journal = {Adv. Math.},
	Number = {1},
	Pages = {608--640},
	Publisher = {Elsevier},
	Title = {Permutahedra and generalized associahedra},
	Volume = {226},
	Year = {2011}}

@book{Reiner,
	Author = {Reiner, V.},
	Date-Modified = {2019-05-28 17:51:03 +1000},
	Doi = {10.1090/memo/0460},
	Fjournal = {Memoirs of the American Mathematical Society},
	Issn = {0065-9266},
	Journal = {Mem. Amer. Math. Soc.},
	Mrclass = {05E10 (13A50 20F55 52B20)},
	Mrnumber = {1101971},
	Mrreviewer = {Ira Gessel},
	Number = {Vol. 95, No. 460},
	Publisher = {Amer. Math. Soc., Providence, RI},
	Series = {Mem. Amer. Math. Soc.},
	Title = {Quotients of {C}oxeter complexes and {$P$}-partitions},
	Year = {1992},
	Bdsk-Url-1 = {https://doi.org/10.1090/memo/0460}}

@article{Stembridge,
	Author = {Stembridge, J. R.},
	Date-Modified = {2019-05-28 17:51:32 +1000},
	Doi = {10.1016/j.aim.2007.09.002},
	Fjournal = {Advances in Mathematics},
	Issn = {0001-8708},
	Journal = {Adv. Math.},
	Mrclass = {52B22 (06A07)},
	Mrnumber = {2388082},
	Number = {5},
	Pages = {1935--1961},
	Title = {Coxeter cones and their {$h$}-vectors},
	Volume = {217},
	Year = {2008},
	Bdsk-Url-1 = {https://doi.org/10.1016/j.aim.2007.09.002}}

@article{meyer,
	Author = {Meyer, Walter},
	Doi = {10.2307/1996951},
	Fjournal = {Transactions of the American Mathematical Society},
	Issn = {0002-9947},
	Journal = {Trans. Amer. Math. Soc.},
	Mrclass = {52A25},
	Mrnumber = {0338929},
	Mrreviewer = {P. McMullen},
	Pages = {77--86},
	Title = {Indecomposable polytopes},
	Url = {https://doi.org/10.2307/1996951},
	Volume = {190},
	Year = {1974},
	Bdsk-Url-1 = {https://doi.org/10.2307/1996951}}

@article{derksen-fink,
	Author = {Derksen, Harm and Fink, Alex},
	Doi = {10.1016/j.aim.2010.04.016},
	Fjournal = {Advances in Mathematics},
	Issn = {0001-8708},
	Journal = {Adv. Math.},
	Mrclass = {52B40 (05B35)},
	Mrnumber = {2680193},
	Mrreviewer = {Jakayla R. Robbins},
	Number = {4},
	Pages = {1840--1892},
	Title = {Valuative invariants for polymatroids},
	Url = {https://doi.org/10.1016/j.aim.2010.04.016},
	Volume = {225},
	Year = {2010},
	Bdsk-Url-1 = {https://doi.org/10.1016/j.aim.2010.04.016}}

@incollection{edmonds,
	Author = {Edmonds, Jack},
	Booktitle = {Combinatorial {S}tructures and their {A}pplications ({P}roc. {C}algary {I}nternat. {C}onf., {C}algary, {A}lta., 1969)},
	Mrclass = {05.35},
	Mrnumber = {0270945},
	Mrreviewer = {A. W. Ingleton},
	Pages = {69--87},
	Publisher = {Gordon and Breach, New York},
	Title = {Submodular functions, matroids, and certain polyhedra},
	Year = {1970}}

@book{Oxl11,
	Author = {Oxley, James},
	Doi = {10.1093/acprof:oso/9780198566946.001.0001},
	Edition = {Second},
	Isbn = {978-0-19-960339-8},
	Mrclass = {05-01 (05B35 90C27)},
	Mrnumber = {2849819},
	Mrreviewer = {Maruti M. Shikare},
	Pages = {xiv+684},
	Publisher = {Oxford University Press, Oxford},
	Series = {Oxford Graduate Texts in Mathematics},
	Title = {Matroid theory},
	Url = {https://doi.org/10.1093/acprof:oso/9780198566946.001.0001},
	Volume = {21},
	Year = {2011},
	Bdsk-Url-1 = {https://doi.org/10.1093/acprof:oso/9780198566946.001.0001}}

@book{BGW03,
	Author = {Borovik, A.-V. and Gelfand, I. M. and White, N.},
	Date-Modified = {2019-05-28 17:48:43 +1000},
	Isbn = {0-8176-3764-8},
	Number = {216},
	Publisher = {Birkh\"auser, Boston},
	Series = {Progress in Mathematics},
	Title = {Coxeter Matroids},
	Year = {2003}}

@article{shep,
	Author = {Shephard, G. C.},
	Doi = {10.1112/S0025579300003995},
	Fjournal = {Mathematika. A Journal of Pure and Applied Mathematics},
	Issn = {0025-5793},
	Journal = {Mathematika},
	Mrclass = {52.10},
	Mrnumber = {0172176},
	Mrreviewer = {B. Gr\"{u}nbaum},
	Pages = {89--95},
	Title = {Decomposable convex polyhedra},
	Url = {https://doi.org/10.1112/S0025579300003995},
	Volume = {10},
	Year = {1963},
	Bdsk-Url-1 = {https://doi.org/10.1112/S0025579300003995}}

@article{extreme,
	Author = {Nguyen, Hien Quang},
	Doi = {10.2307/1997813},
	Fjournal = {Transactions of the American Mathematical Society},
	Issn = {0002-9947},
	Journal = {Trans. Amer. Math. Soc.},
	Mrclass = {05B35},
	Mrnumber = {0491269},
	Mrreviewer = {Thomas Brylawski},
	Pages = {355--383},
	Title = {Semimodular functions and combinatorial geometries},
	Url = {https://doi.org/10.2307/1997813},
	Volume = {238},
	Year = {1978},
	Bdsk-Url-1 = {https://doi.org/10.2307/1997813}}

@article{econ,
	Author = {Studen\'{y}, Milan and Kroupa, Tom\'{a}\v{s}},
	Doi = {10.1016/j.dam.2016.01.019},
	Fjournal = {Discrete Applied Mathematics. The Journal of Combinatorial Algorithms, Informatics and Computational Sciences},
	Issn = {0166-218X},
	Journal = {Discrete Appl. Math.},
	Mrclass = {91A12},
	Mrnumber = {3490436},
	Pages = {122--151},
	Title = {Core-based criterion for extreme supermodular functions},
	Url = {https://doi.org/10.1016/j.dam.2016.01.019},
	Volume = {206},
	Year = {2016},
	Bdsk-Url-1 = {https://doi.org/10.1016/j.dam.2016.01.019}}

@article{ggms,
	Author = {Gelfand, I. M. and Goresky, R. M. and MacPherson, R. D. and Serganova, V. V.},
	Doi = {10.1016/0001-8708(87)90059-4},
	Fjournal = {Advances in Mathematics},
	Issn = {0001-8708},
	Journal = {Adv. in Math.},
	Mrclass = {14M15 (05B35 22E45 22E70 32C38 32C45 32M10)},
	Mrnumber = {877789},
	Mrreviewer = {Hiroaki Terao},
	Number = {3},
	Pages = {301--316},
	Title = {Combinatorial geometries, convex polyhedra, and {S}chubert cells},
	Url = {https://doi.org/10.1016/0001-8708(87)90059-4},
	Volume = {63},
	Year = {1987},
	Bdsk-Url-1 = {https://doi.org/10.1016/0001-8708(87)90059-4}}

@book{toric,
	Author = {Cox, D.-A. and Little, J.-B. and Schenck, H.-K.},
	Date-Modified = {2019-05-28 17:49:01 +1000},
	Doi = {10.1090/gsm/124},
	Isbn = {978-0-8218-4819-7},
	Mrclass = {14M25 (05A15 05E45 52B12)},
	Mrnumber = {2810322},
	Mrreviewer = {Ivan Arzhantsev},
	Number = {124},
	Publisher = {Amer. Math. Soc., Providence, RI},
	Series = {Graduate Studies in Mathematics},
	Title = {Toric Varieties},
	Year = {2011},
	Bdsk-Url-1 = {https://doi.org/10.1090/gsm/124}}

@article{permutohedra,
	Author = {Postnikov, A.},
	Doi = {10.1093/imrn/rnn153},
	Fjournal = {International Mathematics Research Notices. IMRN},
	Issn = {1073-7928},
	Journal = {Int. Math. Res. Not. IMRN},
	Mrclass = {05E30},
	Mrnumber = {2487491},
	Number = {6},
	Pages = {1026--1106},
	Title = {Permutohedra, associahedra, and beyond},
	Url = {https://doi.org/10.1093/imrn/rnn153},
	Year = {2009},
	Bdsk-Url-1 = {https://doi.org/10.1093/imrn/rnn153}}

@article{faces,
	Author = {Postnikov, A. and Reiner, V. and Williams, L.},
	Fjournal = {Documenta Mathematica},
	Issn = {1431-0635},
	Journal = {Doc. Math.},
	Mrclass = {05E30 (05A15)},
	Mrnumber = {2520477},
	Pages = {207--273},
	Title = {Faces of generalized permutohedra},
	Volume = {13},
	Year = {2008}}

@article{deformation,
	Author = {Castillo, Federico and Liu, Fu},
	Journal = {https://arxiv.org/abs/1710.01899},
	Title = {Deformation Cones of nested Braid fans}}

@article{aa,
	Author = {Aguiar, Marcelo and Ardila, Federico},
	Journal = {https://arxiv.org/abs/1709.07504},
	Title = {Hopf monoids and generalized permutahedra}}

@article{indecomposable,
	Author = {McMullen, Peter},
	Doi = {10.1007/BF02771695},
	Fjournal = {Israel Journal of Mathematics},
	Issn = {0021-2172},
	Journal = {Israel J. Math.},
	Mrclass = {52A25},
	Mrnumber = {917362},
	Mrreviewer = {Juan Garc\'{i}a Laguna},
	Number = {3},
	Pages = {321--323},
	Title = {Indecomposable convex polytopes},
	Url = {https://doi.org/10.1007/BF02771695},
	Volume = {58},
	Year = {1987},
	Bdsk-Url-1 = {https://doi.org/10.1007/BF02771695}}

@article{extremerays,
	Author = {Studen\'{y}, Milan and Kroupa, Tom\'{a}\v{s}},
	Doi = {10.1016/j.dam.2016.01.019},
	Fjournal = {Discrete Applied Mathematics. The Journal of Combinatorial Algorithms, Informatics and Computational Sciences},
	Issn = {0166-218X},
	Journal = {Discrete Appl. Math.},
	Mrclass = {91A12},
	Mrnumber = {3490436},
	Pages = {122--151},
	Title = {Core-based criterion for extreme supermodular functions},
	Url = {https://doi.org/10.1016/j.dam.2016.01.019},
	Volume = {206},
	Year = {2016},
	Bdsk-Url-1 = {https://doi.org/10.1016/j.dam.2016.01.019}}

@article{alcoved,
	Author = {Lam, Thomas and Postnikov, Alexander},
	Doi = {10.1007/s00454-006-1294-3},
	Fjournal = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	Issn = {0179-5376},
	Journal = {Discrete Comput. Geom.},
	Mrclass = {52B12 (52B40)},
	Mrnumber = {2352704},
	Mrreviewer = {Jes\'us A. De Loera},
	Number = {3},
	Pages = {453--478},
	Title = {Alcoved polytopes. {I}},
	Url = {https://doi.org/10.1007/s00454-006-1294-3},
	Volume = {38},
	Year = {2007},
	Bdsk-Url-1 = {https://doi.org/10.1007/s00454-006-1294-3}}

@article{matroidvolumes,
	Author = {Ardila, Federico and Benedetti, Carolina and Doker, Jeffrey},
	Doi = {10.1007/s00454-009-9232-9},
	Fjournal = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	Issn = {0179-5376},
	Journal = {Discrete Comput. Geom.},
	Mrclass = {52B40 (05B35)},
	Mrnumber = {2610473},
	Mrreviewer = {Sonoko Moriyama},
	Number = {4},
	Pages = {841--854},
	Title = {Matroid polytopes and their volumes},
	Url = {https://doi.org/10.1007/s00454-009-9232-9},
	Volume = {43},
	Year = {2010},
	Bdsk-Url-1 = {https://doi.org/10.1007/s00454-009-9232-9}}

@book{reflection,
	Author = {Humphreys, J.-E.},
	Doi = {10.1017/CBO9780511623646},
	Isbn = {0-521-37510-X},
	Mrclass = {20-02 (20F32 20F55 20G15 20H15)},
	Mrnumber = {1066460},
	Mrreviewer = {Louis Solomon},
	Pages = {xii+204},
	Publisher = {Cambridge University Press, Cambridge},
	Series = {Cambridge Studies in Advanced Mathematics},
	Title = {Reflection groups and {C}oxeter groups},
	Url = {https://doi.org/10.1017/CBO9780511623646},
	Volume = {29},
	Year = {1990},
	Bdsk-Url-1 = {https://doi.org/10.1017/CBO9780511623646}}

@book{grunbaum,
	Author = {Gr\"{u}nbaum, Branko},
	Doi = {10.1007/978-1-4613-0019-9},
	Edition = {Second},
	Isbn = {0-387-00424-6; 0-387-40409-0},
	Mrclass = {52-01 (52Bxx)},
	Mrnumber = {1976856},
	Mrreviewer = {Alexander Zvonkin},
	Note = {Prepared and with a preface by Volker Kaibel, Victor Klee and G\"{u}nter M. Ziegler},
	Pages = {xvi+468},
	Publisher = {Springer-Verlag, New York},
	Series = {Graduate Texts in Mathematics},
	Title = {Convex polytopes},
	Url = {https://doi.org/10.1007/978-1-4613-0019-9},
	Volume = {221},
	Year = {2003},
	Bdsk-Url-1 = {https://doi.org/10.1007/978-1-4613-0019-9}}