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@article {AHK,
	AUTHOR = {Adiprasito, Karim and Huh, June and Katz, Eric},
	TITLE = {Hodge theory for combinatorial geometries},
	JOURNAL = {Ann. of Math. (2)},
	FJOURNAL = {Annals of Mathematics. Second Series},
	VOLUME = {188},
	YEAR = {2018},
	NUMBER = {2},
	PAGES = {381--452},
	ISSN = {0003-486X},
	MRCLASS = {05B35 (05E99 14C25 14T05)},
	MRNUMBER = {3862944},
	MRREVIEWER = {Zvi Rosen},
}

@misc{ALOV,
	AUTHOR  = {Anari, N. and Liu, K. and Oveis~Gharan, S. and Vinzant, C.},
	TITLE   = {Log-concave polynomials~III: Mason's
	ultra-log-concavity conjecture for independent sets of matroids},
	YEAR    = {2018},
	eprinttype = {arXiv},
	eprint = {1811.01600},
}



@incollection {Bra,
	AUTHOR = {Br\"{a}nd\'{e}n, Petter},
	TITLE = {Unimodality, log-concavity, real-rootedness and beyond},
	BOOKTITLE = {Handbook of enumerative combinatorics},
	PAGES = {437--483},
	PUBLISHER = {CRC Press, Boca Raton, FL},
	YEAR = {2015},
	MRCLASS = {05Axx (05D40 05E10)},
	MRNUMBER = {3409348},
}

@incollection {BrW,
	AUTHOR = {Brightwell,~G. and West,~D.},
	TITLE = {Partially ordered sets},
	BOOKTITLE = {Handbook of enumerative combinatorics},
	PAGES = {717--752},
	PUBLISHER = {CRC Press, Boca Raton, FL},
	YEAR = {2000},
}




@article {BH,
	AUTHOR = {Br\"{a}nd\'{e}n, Petter and Huh, June},
	TITLE = {Lorentzian polynomials},
	JOURNAL = {Ann. of Math. (2)},
	FJOURNAL = {Annals of Mathematics. Second Series},
	VOLUME = {192},
	YEAR = {2020},
	NUMBER = {3},
	PAGES = {821--891},
	ISSN = {0003-486X},
	MRCLASS = {52B40 (05A20 14T15)},
	MRNUMBER = {4172622},
	MRREVIEWER = {Trygve Johnsen},
}

@incollection {BZ,
	AUTHOR = {Bj\"{o}rner, Anders and Ziegler, G\"{u}nter M.},
	TITLE = {Introduction to greedoids},
	BOOKTITLE = {Matroid applications},
	PAGES = {284--357},
	PUBLISHER = {Cambridge Univ. Press, Cambridge},
	YEAR = {1992},
	MRCLASS = {05B35 (90C27)},
	MRNUMBER = {1165545},
}


@article {Bre,
	AUTHOR = {Brenti, Francesco},
	TITLE = {Unimodal, log-concave and {P}\'{o}lya frequency sequences in
	combinatorics},
	JOURNAL = {Mem. Amer. Math. Soc.},
	FJOURNAL = {Memoirs of the American Mathematical Society},
	VOLUME = {81},
	YEAR = {1989},
	NUMBER = {413},
	PAGES = {viii+106},
	ISSN = {0065-9266},
	MRCLASS = {05A15 (05A10 05A20)},
	MRNUMBER = {963833},
	MRREVIEWER = {Ira Gessel}
}

@incollection {Bre2,
	AUTHOR = {Brenti, Francesco},
	TITLE = {Log-concave and unimodal sequences in algebra, combinatorics,
	and geometry: an update},
	BOOKTITLE = {Jerusalem combinatorics '93},
	PAGES = {71--89},
	PUBLISHER = {Amer. Math. Soc., Providence, RI},
	YEAR = {1994},
	MRCLASS = {05A20 (05-02)},
	MRNUMBER = {1310575},
	MRREVIEWER = {Christian Krattenthaler},
}

@article {CFG,
	AUTHOR = {Chung, F. R. K. and Fishburn, P. C. and Graham, R. L.},
	TITLE = {On unimodality for linear extensions of partial orders},
	JOURNAL = {SIAM J. Algebraic Discrete Methods},
	FJOURNAL = {Society for Industrial and Applied Mathematics. Journal on
	Algebraic and Discrete Methods},
	VOLUME = {1},
	YEAR = {1980},
	NUMBER = {4},
	PAGES = {405--410},
	ISSN = {0196-5212},
	MRCLASS = {06A10 (90A06)},
	MRNUMBER = {593850},
	MRREVIEWER = {S. V. Ovchinnikov},
}


@misc{CP,
	AUTHOR  = {Chan, Swee Hong and Pak, Igor},
	TITLE   = {Log-concave poset inequalities},
	YEAR    = {2021},
	eprinttype = {arXiv},
	eprint = {2110.10740},
	primaryClass = {math.CO},

}


@misc{CP2,
	AUTHOR  = {Chan, Swee Hong and Pak, Igor},
	TITLE   = {Introduction to the combinatorial atlas},
	YEAR    = {2022},
	eprinttype = {arXiv},
	eprint = {2203.01533},
	primaryClass = {math.CO},
	
}


@article{CPP2,
	AUTHOR  = {Chan, Swee Hong and Pak, Igor and Panova, Greta},
	TITLE   = {The cross-product conjecture for width two posets},
	JOURNAL = {Trans. Amer. Math. Soc.},
    note = {To appear},
	archivePrefix = {arXiv},
	eprint = {2104.09009},
    year = {2021},
	primaryClass = {math.CO},
	
}

@inproceedings {Edm,
	AUTHOR = {Edmonds, Jack},
	TITLE = {Submodular functions, matroids, and certain polyhedra},
	BOOKTITLE = {Combinatorial {S}tructures and their {A}pplications},
	PAGES = {69--87},
	PUBLISHER = {Gordon and Breach, New York},
	YEAR = {1970},
	MRCLASS = {05.35},
	MRNUMBER = {0270945},
	MRREVIEWER = {A. W. Ingleton},
}


@article {EH,
	AUTHOR = {Eur, Christopher and Huh, June},
	TITLE = {Logarithmic concavity for morphisms of matroids},
	JOURNAL = {Adv. Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {367},
	YEAR = {2020},
	PAGES = {No.~107094, 19},
	ISSN = {0001-8708},
	MRCLASS = {05B35 (52B40)},
	MRNUMBER = {4078485},
	MRREVIEWER = {Xiu Xin},
}

@article {HH,
	AUTHOR = {Herzog, J\"{u}rgen and Hibi, Takayuki},
	TITLE = {Discrete polymatroids},
	JOURNAL = {J. Algebraic Combin.},
	FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
	VOLUME = {16},
	YEAR = {2002},
	NUMBER = {3},
	PAGES = {239--268 (2003)},
	ISSN = {0925-9899},
	MRCLASS = {52B40 (05B35 13H10 14M25)},
	MRNUMBER = {1957102},
	MRREVIEWER = {Edward B. Swartz},
}



@inproceedings {Huh,
	AUTHOR = {Huh, June},
	TITLE = {Combinatorial applications of the {H}odge-{R}iemann relations},
	BOOKTITLE = {Proc. ICM Rio de Janeiro, vol.~IV},
	PAGES = {3093--3111},
	PUBLISHER = {World Sci. Publ., Hackensack, NJ},
	YEAR = {2018},
	MRCLASS = {05A20},
	MRNUMBER = {3966524},
}

@article {HSW,
	AUTHOR = {Huh, June and Schr\"oter, B. and  Wang, B. },
	TITLE = {Correlation bounds for fields and matroids},
	JOURNAL = {Jour.\  EMS},
	PAGES = {1335–1351},
	VOLUME={24},
	YEAR={2022},
}

@book {KLS,
	AUTHOR = {Korte, Bernhard and Lov\'{a}sz, L\'{a}szl\'{o} and Schrader, Rainer},
	TITLE = {Greedoids},
	PUBLISHER = {Springer-Verlag, Berlin},
	YEAR = {1991},
	PAGES = {viii+211},
	ISBN = {3-540-18190-3},
	MRCLASS = {90-02 (05B35 90C10 90C27)},
	MRNUMBER = {1183735},
	MRREVIEWER = {Ulrich Faigle},
}


@inproceedings {Mas,
	AUTHOR = {Mason, J. H.},
	TITLE = {Matroids: unimodal conjectures and {M}otzkin's theorem},
	BOOKTITLE = {{P}roc. {C}onf. {C}ombinatorial {M}ath.,
	{M}ath. {I}nst., {O}xford},
	PAGES = {207--220},
	YEAR = {1972},
	MRCLASS = {05B35},
	MRNUMBER = {0349445},
	MRREVIEWER = {W. Dorfler},
}

@article {MNY,
	AUTHOR = {Murai, Satoshi and Nagaoka, Takahiro and Yazawa, Akiko},
	TITLE = {Strictness of the log-concavity of generating polynomials of
	matroids},
	JOURNAL = {J. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A},
	VOLUME = {181},
	YEAR = {2021},
	PAGES = {No.~105351, 22},
	ISSN = {0097-3165},
	MRCLASS = {05B35},
	MRNUMBER = {4223331},
}

@book {Schr,
	AUTHOR = {Schrijver, Alexander},
	TITLE = {Combinatorial optimization. {P}olyhedra and efficiency. {V}ol.
	{B}},
	PUBLISHER = {Springer-Verlag, Berlin},
	YEAR = {2003},
	PAGES = {i--xxxiv and 649--1217},
	ISBN = {3-540-44389-4},
	MRCLASS = {90-02 (05-02 52B55 68Q25 68R10 90C27 90C35 90C57)},
	MRNUMBER = {1956925},
	MRREVIEWER = {Alexander I. Barvinok},
}

@article {SvH19,
	AUTHOR = {Shenfeld, Yair and van Handel, Ramon},
	TITLE = {Mixed volumes and the {B}ochner method},
	JOURNAL = {Proc. Amer. Math. Soc.},
	FJOURNAL = {Proceedings of the American Mathematical Society},
	VOLUME = {147},
	YEAR = {2019},
	NUMBER = {12},
	PAGES = {5385--5402},
	ISSN = {0002-9939},
	MRCLASS = {52A39 (52A40 58J50)},
	MRNUMBER = {4021097},
	MRREVIEWER = {Judit Abardia-Ev\'{e}quoz},
}

@article{SvH,
	AUTHOR  = {Shenfeld, Y. and van Handel, R.},
	TITLE   = {The extremals of the Alexandrov--Fenchel inequality for convex polytopes},
	JOURNAL = {Acta. Math.},
	note = {To appear},
	archivePrefix = {arXiv},
	eprint = {2011.04059},
    year = {2020},
	primaryClass = {math.CO},	
}



@article {Sta,
	AUTHOR = {Stanley, Richard P.},
	TITLE = {Two combinatorial applications of the {A}leksandrov-{F}enchel
	inequalities},
	JOURNAL = {J. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A},
	VOLUME = {31},
	YEAR = {1981},
	NUMBER = {1},
	PAGES = {56--65},
	ISSN = {0097-3165},
	MRCLASS = {52A37 (05B35 06A10)},
	MRNUMBER = {626441},
	MRREVIEWER = {Kit Hanes},
}


@incollection {Sta2,
	AUTHOR = {Stanley, Richard P.},
	TITLE = {Log-concave and unimodal sequences in algebra, combinatorics,
	and geometry},
	BOOKTITLE = {Graph theory and its applications},
	PAGES = {500--535},
	PUBLISHER = {New York Acad. Sci., New York},
	YEAR = {1989},
	MRCLASS = {05E15 (05E10 20C15 52B20)},
	MRNUMBER = {1110850},
	MRREVIEWER = {L. Bruce Richmond},
}


@incollection {Tro,
	AUTHOR = {Trotter, William T.},
	TITLE = {Partially ordered sets},
	BOOKTITLE = {Handbook of combinatorics, {V}ol. 1, 2},
	PAGES = {433--480},
	PUBLISHER = {Elsevier Sci. B. V., Amsterdam},
	YEAR = {1995},
	MRCLASS = {06A07 (06A06)},
	MRNUMBER = {1373664},
	MRREVIEWER = {Graham Brightwell},
}