@article{AHK17, Author = {Adiprasito, Karim and Huh, June and Katz, Eric}, Date-Added = {2019-04-25 14:12:03 +0300}, Date-Modified = {2019-04-25 14:12:03 +0300}, Doi = {10.1090/noti1463}, Fjournal = {Notices of the American Mathematical Society}, Issn = {0002-9920}, Journal = {Notices Amer. Math. Soc.}, Mrclass = {05B35 (14C30 52B40)}, Mrnumber = {3586249}, Mrreviewer = {Ren Ding}, Number = {1}, Pages = {26--30}, Title = {Hodge theory of matroids}, Volume = {64}, Year = {2017}, Bdsk-Url-1 = {https://mathscinet.ams.org/mathscinet-getitem?mr=3586249}} @article{AHK18, author={Adiprasito, Karim and Huh, June and Katz, Eric}, title={{Hodge Theory for combinatorial geometries}}, journal={Annals of Mathematics}, year={2018}, volume={188}, pages={381--452}, } @article {AA17, AUTHOR = {Aguiar, Marcelo and Ardila, Federico}, TITLE = {Hopf monoids and generalized permutahedra}, url = {https://arxiv.org/abs/1709.07504}, YEAR = {2017} } @article {AK06, AUTHOR = {Ardila, Federico and Klivans, Caroline J.}, TITLE = {The {B}ergman complex of a matroid and phylogenetic trees}, JOURNAL = {J. Combin. Theory Ser. B}, FJOURNAL = {Journal of Combinatorial Theory. Series B}, VOLUME = {96}, YEAR = {2006}, NUMBER = {1}, PAGES = {38--49}, ISSN = {0095-8956}, MRCLASS = {05B35}, MRNUMBER = {2185977}, MRREVIEWER = {Neil L. White}, DOI = {10.1016/j.jctb.2005.06.004}, } @misc {ACEP19, AUTHOR = {Ardila, Federico and Castillo, Federico and Eur, Christopher and Postnikov, Alex}, TITLE = {Coxeter submodular functions and deformations of Coxeter permutahedra}, eprint={1904.11029}, YEAR = {2019} } @article {AR10, AUTHOR = {Allermann, Lars and Rau, Johannes}, TITLE = {First steps in tropical intersection theory}, JOURNAL = {Math. Z.}, FJOURNAL = {Mathematische Zeitschrift}, VOLUME = {264}, YEAR = {2010}, NUMBER = {3}, PAGES = {633--670}, ISSN = {0025-5874}, MRCLASS = {14T05 (14C17)}, MRNUMBER = {2591823}, MRREVIEWER = {Joaquim Ro\'{e}}, DOI = {10.1007/s00209-009-0483-1}, } @incollection {AOV18, AUTHOR = {Anari, Nima and Oveis Gharan, Shayan and Vinzant, Cynthia}, TITLE = {Log-concave polynomials, entropy, and a deterministic approximation algorithm for counting bases of matroids}, BOOKTITLE = {59th {A}nnual {IEEE} {S}ymposium on {F}oundations of {C}omputer {S}cience---{FOCS} 2018}, PAGES = {35--46}, PUBLISHER = {IEEE Computer Soc., Los Alamitos, CA}, YEAR = {2018}, MRCLASS = {68W25 (05A15 05B35)}, MRNUMBER = {3899575}, } @article {Bak18, AUTHOR = {Baker, Matthew}, TITLE = {Hodge theory in combinatorics}, JOURNAL = {Bull. Amer. Math. Soc. (N.S.)}, FJOURNAL = {American Mathematical Society. Bulletin. New Series}, VOLUME = {55}, YEAR = {2018}, NUMBER = {1}, PAGES = {57--80}, ISSN = {0273-0979}, MRCLASS = {05B35 (05C31 58A14)}, MRNUMBER = {3737210}, MRREVIEWER = {Michael J. Falk}, DOI = {10.1090/bull/1599}, } @article {BB11, AUTHOR = {Batyrev, Victor and Blume, Mark}, TITLE = {The functor of toric varieties associated with {W}eyl chambers and {L}osev-{M}anin moduli spaces}, JOURNAL = {Tohoku Math. J. (2)}, FJOURNAL = {The Tohoku Mathematical Journal. Second Series}, VOLUME = {63}, YEAR = {2011}, NUMBER = {4}, PAGES = {581--604}, ISSN = {0040-8735}, MRCLASS = {14M25 (14D20 17B22)}, MRNUMBER = {2872957}, MRREVIEWER = {Martijn Kool}, DOI = {10.2748/tmj/1325886282}, } @article {Bjo92, AUTHOR = {Bjorner, Anders}, TITLE = {The homology and shellability of matroids and geometric lattices}, BOOKTITLE = {Matroid applications}, SERIES = {Encyclopedia Math. Appl.}, VOLUME = {40}, PAGES = {226--283}, PUBLISHER = {Cambridge Univ. Press, Cambridge}, YEAR = {1992}, MRCLASS = {52B40 (05B35 55N99)}, MRNUMBER = {1165544}, MRREVIEWER = {Michel Yves Jambu}, DOI = {10.1017/CBO9780511662041.008}, } @misc{BH19, author={Br\"and\'en, Petter and Huh, June}, title={Lorentzian polynomials}, eprint={1902.03719}, year={2019}, } @book {BH93, AUTHOR = {Bruns, Winfried and Herzog, J\"{u}rgen}, TITLE = {Cohen-{M}acaulay rings}, SERIES = {Cambridge Studies in Advanced Mathematics}, VOLUME = {39}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {1993}, PAGES = {xii+403}, ISBN = {0-521-41068-1}, MRCLASS = {13H10 (13-02)}, MRNUMBER = {1251956}, MRREVIEWER = {Matthew Miller}, } @article{Bri96, author={Brion, Michel}, title={{Piecewise polynomial functions, convex polytopes and enumerative geometry}}, conference={ title={Parameter spaces}, address={Warsaw}, date={1994}, }, book={ series={Banach Center Publ.}, volume={36}, publisher={Polish Acad. Sci. Inst. Math., Warsaw}, }, year={1996}, pages={25--44}, } @article{Bry75, author={Brylawski, Thomas H.}, title={{An affine representation for transversal geometries}}, journal={Studies in Appl. Math.}, volume={54}, year={1975}, number={2}, pages={143--160}, } @article {Bry86, AUTHOR = {Brylawski, Thomas}, TITLE = {Constructions}, BOOKTITLE = {Theory of matroids}, SERIES = {Encyclopedia Math. Appl.}, VOLUME = {26}, PAGES = {127--223}, PUBLISHER = {Cambridge Univ. Press, Cambridge}, YEAR = {1986}, MRCLASS = {05B35}, MRNUMBER = {849396}, DOI = {10.1017/CBO9780511629563.010}, } @article{CLZ16, author={Castillo, Federico and Li, Binglin and Zhang, Naizhen}, title={Representable Chow classes of a product of projective spaces}, eprint={1612.00154}, year={2016}, } @book {CLS11, AUTHOR = {Cox, David A. and Little, John B. and Schenck, Henry K.}, TITLE = {Toric varieties}, SERIES = {Graduate Studies in Mathematics}, VOLUME = {124}, PUBLISHER = {American Mathematical Society, Providence, RI}, YEAR = {2011}, PAGES = {xxiv+841}, ISBN = {978-0-8218-4819-7}, MRCLASS = {14M25 (05A15 05E45 52B12)}, MRNUMBER = {2810322}, MRREVIEWER = {Ivan Arzhantsev}, DOI = {10.1090/gsm/124}, } @article {dCP95, AUTHOR = {De Concini, C. and Procesi, C.}, TITLE = {Wonderful models of subspace arrangements}, JOURNAL = {Selecta Math. (N.S.)}, FJOURNAL = {Selecta Mathematica. New Series}, VOLUME = {1}, YEAR = {1995}, NUMBER = {3}, PAGES = {459--494}, ISSN = {1022-1824}, MRCLASS = {14D99 (32G13 52B30)}, MRNUMBER = {1366622}, MRREVIEWER = {V. Leksin}, DOI = {10.1007/BF01589496}, } @article {Den14, AUTHOR = {Denham, Graham}, TITLE = {Toric and tropical compactifications of hyperplane complements}, JOURNAL = {Ann. Fac. Sci. Toulouse Math. (6)}, FJOURNAL = {Annales de la Facult\'{e} des Sciences de Toulouse. Math\'{e}matiques. S\'{e}rie 6}, VOLUME = {23}, YEAR = {2014}, NUMBER = {2}, PAGES = {297--333}, ISSN = {0240-2963}, MRCLASS = {14N20 (14-02 14M25 14M27 14T05 52B40 52C35)}, MRNUMBER = {3205595}, MRREVIEWER = {G. K. Sankaran}, DOI = {10.5802/afst.1408}, } @article {Dil44, AUTHOR = {Dilworth, R. P.}, TITLE = {Dependence relations in a semi-modular lattice}, JOURNAL = {Duke Math. J.}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {11}, YEAR = {1944}, PAGES = {575--587}, ISSN = {0012-7094}, MRCLASS = {09.1X}, MRNUMBER = {0011287}, MRREVIEWER = {O. Frink}, URL = {http://projecteuclid.org/euclid.dmj/1077472665}, } @misc{Dot19, author = {Dotsenko, Vladimir}, title = {Homotopy invariants for $\overline{\mathcal M}_{0,n}$ via Koszul duality}, eprint={1902.06318}, year = {2019} } @article{Sin04, author = {Singh, D.}, title = {The moduli space of stable N-pointed curves of genus zero}, note={Thesis (Ph.D.)--University of Sheffield}, year = {2004} } @book{CLO07, author={Cox, David and Little, John and O'Shea, Donal}, title={{Ideals, varieties, and algorithms}}, series={Undergraduate Texts in Mathematics}, edition={3}, note={An introduction to computational algebraic geometry and commutative algebra}, publisher={Springer, New York}, year={2007}, pages={xvi+551}, isbn={978-0-387-35650-1}, isbn={0-387-35650-9}, doi={10.1007/978-0-387-35651-8}, } @article{Der09, author={Derksen, Harm}, title={{Symmetric and quasi-symmetric functions associated to polymatroids}}, journal={J. Algebraic Combin.}, volume={30}, year={2009}, number={1}, pages={43--86}, issn={0925-9899}, } @article{DF10, author={Derksen, Harm and Fink, Alex}, title={{Valuative invariants for polymatroids}}, journal={Adv. Math.}, volume={225}, year={2010}, number={4}, pages={1840--1892}, issn={0001-8708}, } @article {EHKR10, AUTHOR = {Etingof, Pavel and Henriques, Andr\'{e} and Kamnitzer, Joel and Rains, Eric M.}, TITLE = {The cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points}, JOURNAL = {Ann. of Math. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {171}, YEAR = {2010}, NUMBER = {2}, PAGES = {731--777}, ISSN = {0003-486X}, MRCLASS = {14H10 (14F99 18D50)}, MRNUMBER = {2630055}, MRREVIEWER = {Orsola Tommasi}, DOI = {10.4007/annals.2010.171.731}, } @article {ELMNP05, AUTHOR = {Ein, L. and Lazarsfeld, R. and Musta\c{t}\v{a}, M. and Nakamaye, M. and Popa, M.}, TITLE = {Asymptotic invariants of line bundles}, JOURNAL = {Pure Appl. Math. Q.}, FJOURNAL = {Pure and Applied Mathematics Quarterly}, VOLUME = {1}, YEAR = {2005}, NUMBER = {2, Special Issue: In memory of Armand Borel. Part 1}, PAGES = {379--403}, ISSN = {1558-8599}, MRCLASS = {14C20}, MRNUMBER = {2194730}, MRREVIEWER = {Alex K\"{u}ronya}, DOI = {10.4310/PAMQ.2005.v1.n2.a8}, } @incollection {Edm70, AUTHOR = {Edmonds, Jack}, TITLE = {Submodular functions, matroids, and certain polyhedra}, BOOKTITLE = {Combinatorial {S}tructures and their {A}pplications ({P}roc. {C}algary {I}nternat. {C}onf., {C}algary, {A}lta., 1969)}, PAGES = {69--87}, PUBLISHER = {Gordon and Breach, New York}, YEAR = {1970}, MRCLASS = {05.35}, MRNUMBER = {0270945}, MRREVIEWER = {A. W. Ingleton}, } @book{Eis94, author={Eisenbud, David}, title={Commutative algebra with a view towards algebraic geometry}, publisher={Springer-Verlag}, year={1994}, isbn={978-1-4612-5350-1} } @book{EH16, author={Eisenbud, David and Harris, Joe}, title={{3264 and all that---a second course in algebraic geometry}}, publisher={Cambridge University Press, Cambridge}, year={2016}, pages={xiv+616}, isbn={978-1-107-60272-4}, } @article {Eur20, AUTHOR = {Eur, Christopher}, TITLE = {Divisors on matroids and their volumes}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {169}, YEAR = {2020}, PAGES = {105135, 31}, ISSN = {0097-3165}, MRCLASS = {05B35 (14C15 14T05)}, MRNUMBER = {4011081}, DOI = {10.1016/j.jcta.2019.105135}, } @article {FMSS95, AUTHOR = {Fulton, W. and MacPherson, R. and Sottile, F. and Sturmfels, B.}, TITLE = {Intersection theory on spherical varieties}, JOURNAL = {J. Algebraic Geom.}, FJOURNAL = {Journal of Algebraic Geometry}, VOLUME = {4}, YEAR = {1995}, NUMBER = {1}, PAGES = {181--193}, ISSN = {1056-3911}, MRCLASS = {14C15 (14C25 14L30)}, MRNUMBER = {1299008}, MRREVIEWER = {Michel Brion}, } @article {FS05, AUTHOR = {Feichtner, Eva Maria and Sturmfels, Bernd}, TITLE = {Matroid polytopes, nested sets and {B}ergman fans}, JOURNAL = {Port. Math. (N.S.)}, FJOURNAL = {Portugaliae Mathematica. Nova S\'{e}rie}, VOLUME = {62}, YEAR = {2005}, NUMBER = {4}, PAGES = {437--468}, ISSN = {0032-5155}, MRCLASS = {05B35 (52B20 52B40 52C35)}, MRNUMBER = {2191630}, MRREVIEWER = {Neil L. White}, } @article{FY04, author={Feichtner, Eva Maria and Yuzvinsky, Sergey}, title={{Chow rings of toric varieties defined by atomic lattices}}, journal={Invent. Math.}, volume={155}, year={2004}, number={3}, pages={515--536}, issn={0020-9910}, } @article{FK10, Author = {Fleming, Balin and Karu, Kalle}, Date-Added = {2019-05-15 10:25:08 -0700}, Date-Modified = {2019-05-15 10:25:08 -0700}, Doi = {10.1007/s10801-009-0212-1}, Fjournal = {Journal of Algebraic Combinatorics. An International Journal}, Issn = {0925-9899}, Journal = {J. Algebraic Combin.}, Mrclass = {52B05 (14M25)}, Mrnumber = {2661416}, Mrreviewer = {Hendrik S\"{u}\ss}, Number = {2}, Pages = {227--239}, Title = {Hard {L}efschetz theorem for simple polytopes}, Volume = {32}, Year = {2010}, Bdsk-Url-1 = {https://mathscinet.ams.org/mathscinet-getitem?mr=2661416}} @article {FS97, AUTHOR = {Fulton, William and Sturmfels, Bernd}, TITLE = {Intersection theory on toric varieties}, JOURNAL = {Topology}, FJOURNAL = {Topology. An International Journal of Mathematics}, VOLUME = {36}, YEAR = {1997}, NUMBER = {2}, PAGES = {335--353}, ISSN = {0040-9383}, MRCLASS = {14M25 (14C17 52B20)}, MRNUMBER = {1415592}, MRREVIEWER = {Michel Brion}, DOI = {10.1016/0040-9383(96)00016-X}, } @book{Ful93, author={Fulton, William}, title={{Introduction to toric varieties}}, series={Annals of Mathematics Studies}, volume={131}, note={The William H. Roever Lectures in Geometry}, publisher={Princeton University Press, Princeton, NJ}, year={1993}, pages={xii+157}, isbn={0-691-00049-2}, } @book {Ful98, AUTHOR = {Fulton, William}, TITLE = {Intersection theory}, SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]}, VOLUME = {2}, EDITION = {Second}, PUBLISHER = {Springer-Verlag, Berlin}, YEAR = {1998}, PAGES = {xiv+470}, ISBN = {3-540-62046-X; 0-387-98549-2}, MRCLASS = {14C17 (14-02)}, MRNUMBER = {1644323}, DOI = {10.1007/978-1-4612-1700-8}, } @article{GGMS87, author={Gelfand, I. M. and Goresky, R. M. and MacPherson, R. D. and Serganova, V. V.}, title={{Combinatorial geometries, convex polyhedra, and Schubert cells}}, journal={Adv. in Math.}, volume={63}, year={1987}, number={3}, pages={301--316}, issn={0001-8708}, } @article{Hal35, author = {Hall, P.}, title = {On Representatives of Subsets}, journal = {Journal of the London Mathematical Society}, volume = {s1-10}, number = {1}, pages = {26-30}, doi = {10.1112/jlms/s1-10.37.26}, year = {1935} } @book {Hat02, AUTHOR = {Hatcher, Allen}, TITLE = {Algebraic topology}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2002}, PAGES = {xii+544}, ISBN = {0-521-79160-X; 0-521-79540-0}, MRCLASS = {55-01 (55-00)}, MRNUMBER = {1867354}, MRREVIEWER = {Donald W. Kahn}, } @article{Ham17, author={Hampe, Simon}, title={{The intersection ring of matroids}}, journal={J. Combin. Theory Ser. B}, volume={122}, year={2017}, pages={578--614}, issn={0095-8956}, } @article{Her72, Author = {Heron, A. P.}, Booktitle = {Combinatorics ({P}roc. {C}onf. {C}ombinatorial {M}ath., {M}ath. {I}nst., {O}xford, 1972)}, Date-Added = {2019-04-24 15:21:27 +0300}, Date-Modified = {2019-04-24 15:21:27 +0300}, Mrclass = {05B35}, Mrnumber = {0340058}, Mrreviewer = {Ann Miller}, Pages = {164--202}, Publisher = {Inst. Math. Appl., Southend-on-Sea}, Title = {Matroid polynomials}, Url = {https://mathscinet.ams.org/mathscinet-getitem?mr=0340058}, Year = {1972}, Bdsk-Url-1 = {https://mathscinet.ams.org/mathscinet-getitem?mr=0340058}} @article {Hig68, AUTHOR = {Higgs, D. A.}, TITLE = {Strong maps of geometries}, JOURNAL = {J. Combinatorial Theory}, VOLUME = {5}, YEAR = {1968}, PAGES = {185--191}, MRCLASS = {06.40 (05.00)}, MRNUMBER = {0231761}, MRREVIEWER = {R. A. Brualdi}, } @article{Huh12, Author = {Huh, June}, Date-Added = {2019-04-24 15:33:21 +0300}, Date-Modified = {2019-04-24 15:33:21 +0300}, Doi = {10.1090/S0894-0347-2012-00731-0}, Fjournal = {Journal of the American Mathematical Society}, Issn = {0894-0347}, Journal = {J. Amer. Math. Soc.}, Mrclass = {14B05 (05B35 14C17)}, Mrnumber = {2904577}, Mrreviewer = {Paolo Aluffi}, Number = {3}, Pages = {907--927}, Title = {Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs}, Volume = {25}, Year = {2012}, Bdsk-Url-1 = {https://mathscinet.ams.org/mathscinet-getitem?mr=2904577}} @article{Huh18a, author={Huh, June}, title={Combinatorial applications of the Hodge-Riemann relations}, journal={Proc. Int. Cong. of Math. Rio de Janeiro}, pages={3079--3098}, year={2018}, volume={3} } @book{Huh14, author={Huh, June}, title={{Rota's conjecture and positivity of algebraic cycles in permutohedral varieties}}, note={Thesis (Ph.D.)--University of Michigan}, publisher={ProQuest LLC, Ann Arbor, MI}, year={2014}, pages={73}, isbn={978-1321-50396-8}, } @article{Huh18, author={Huh, June}, title={{Tropical geometry of matroids}}, journal={Current Developments in Mathematics 2016}, pages={1--46}, year={2018}, } @article{HK12, author={Huh, June and Katz, Eric}, title={{Log-concavity of characteristic polynomials and the Bergman fan of matroids}}, journal={Math. Ann.}, volume={354}, year={2012}, number={3}, pages={1103--1116}, issn={0025-5831}, } @misc{HRS18, author={Hameister, Thomas and Rao, Sujit and Simpson, Connor}, title={Chow Rings of Vector Space Matroids}, eprint={1802.04241}, date={2018} } @misc{HSW18, author={Huh, June and Schr\"oter, Benjamin and Wang, Botong}, title={Correlation bounds for fields and matroids}, eprint={1806.02675}, date={2018} } @article {HW17, 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}, ISSN = {0001-5962}, MRCLASS = {05A15 (52C10)}, MRNUMBER = {3733101}, DOI = {10.4310/ACTA.2017.v218.n2.a2}, } @article {JSS19, AUTHOR = {Jell, Philipp and Shaw, Kristin and Smacka, Jascha}, TITLE = {Superforms, tropical cohomology, and {P}oincar\'{e} duality}, JOURNAL = {Adv. Geom.}, FJOURNAL = {Advances in Geometry}, VOLUME = {19}, YEAR = {2019}, NUMBER = {1}, PAGES = {101--130}, ISSN = {1615-715X}, MRCLASS = {14T05}, MRNUMBER = {3903579}, DOI = {10.1515/advgeom-2018-0006}, } @article {JY16, AUTHOR = {Jensen, Anders and Yu, Josephine}, TITLE = {Stable intersections of tropical varieties}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {43}, YEAR = {2016}, NUMBER = {1}, PAGES = {101--128}, ISSN = {0925-9899}, MRCLASS = {14T05}, MRNUMBER = {3439302}, MRREVIEWER = {D. A. Stepanov}, DOI = {10.1007/s10801-015-0627-9}, } @article{Kat16, author={Katz, Eric}, title={{Matroid theory for algebraic geometers}}, conference={ title={Nonarchimedean and tropical geometry}, }, book={ series={Simons Symp.}, publisher={Springer, [Cham]}, }, year={2016}, pages={435--517}, } @article {KK78, AUTHOR = {Kelly, Douglas G. and Kennedy, Daniel}, TITLE = {The {H}iggs factorization of a geometric strong map}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {22}, YEAR = {1978}, NUMBER = {2}, PAGES = {139--146}, ISSN = {0012-365X}, MRCLASS = {05B25}, MRNUMBER = {523300}, MRREVIEWER = {Jeremy Dawson}, DOI = {10.1016/0012-365X(78)90121-8}, } @article{KRS99, Author = {Kook, W. and Reiner, V. and Stanton, D.}, Date-Added = {2019-04-25 15:16:13 +0300}, Date-Modified = {2019-04-25 15:16:13 +0300}, Doi = {10.1006/jctb.1998.1888}, Fjournal = {Journal of Combinatorial Theory. Series B}, Issn = {0095-8956}, Journal = {J. Combin. Theory Ser. B}, Mrclass = {05B35}, Mrnumber = {1699230}, Mrreviewer = {J. M. S. Sim\~{o}es-Pereira}, Number = {2}, Pages = {297--300}, Title = {A convolution formula for the {T}utte polynomial}, Volume = {76}, Year = {1999}, Bdsk-Url-1 = {https://mathscinet.ams.org/mathscinet-getitem?mr=1699230}} @article{Kun86, author={Kung, Joseph P. S.}, title={{Strong maps}}, conference={ title={Theory of matroids}, }, book={ series={Encyclopedia Math. Appl.}, volume={26}, publisher={Cambridge Univ. Press, Cambridge}, }, year={1986}, pages={224--253}, } @book {Laz04, AUTHOR = {Lazarsfeld, Robert}, TITLE = {Positivity in algebraic geometry. {I}}, SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]}, VOLUME = {48}, NOTE = {Classical setting: line bundles and linear series}, PUBLISHER = {Springer-Verlag, Berlin}, YEAR = {2004}, PAGES = {xviii+387}, ISBN = {3-540-22533-1}, MRCLASS = {14-02 (14C20)}, MRNUMBER = {2095471}, MRREVIEWER = {Mihnea Popa}, DOI = {10.1007/978-3-642-18808-4}, } @article {Len13, AUTHOR = {Lenz, Matthias}, TITLE = {The {$f$}-vector of a representable-matroid complex is log-concave}, JOURNAL = {Adv. in Appl. Math.}, FJOURNAL = {Advances in Applied Mathematics}, VOLUME = {51}, YEAR = {2013}, NUMBER = {5}, PAGES = {543--545}, ISSN = {0196-8858}, MRCLASS = {05B35 (05A20 05C31 05E45)}, MRNUMBER = {3118543}, MRREVIEWER = {John J. Watkins}, DOI = {10.1016/j.aam.2013.07.001}, } @article {LdMRS20, AUTHOR = {L\'{o}pez de Medrano, Luc\'{\i}a and Rinc\'{o}n, Felipe and Shaw, Kristin}, TITLE = {Chern-{S}chwartz-{M}ac{P}herson cycles of matroids}, JOURNAL = {Proc. Lond. Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {120}, YEAR = {2020}, NUMBER = {1}, PAGES = {1--27}, ISSN = {0024-6115}, MRCLASS = {14C17 (05B35 52C35)}, MRNUMBER = {3999674}, MRREVIEWER = {Shaheen Nazir}, DOI = {10.1112/plms.12278}, } @article {LM00, AUTHOR = {Losev, A. and Manin, Y.}, TITLE = {New moduli spaces of pointed curves and pencils of flat connections}, NOTE = {Dedicated to William Fulton on the occasion of his 60th birthday}, JOURNAL = {Michigan Math. J.}, FJOURNAL = {Michigan Mathematical Journal}, VOLUME = {48}, YEAR = {2000}, PAGES = {443--472}, ISSN = {0026-2285}, MRCLASS = {14N35 (14H10 53D45)}, MRNUMBER = {1786500}, MRREVIEWER = {Andrew Kresch}, DOI = {10.1307/mmj/1030132728}, } @book{MS15, author={Maclagan, Diane and Sturmfels, Bernd}, title={{Introduction to tropical geometry}}, series={Graduate Studies in Mathematics}, volume={161}, publisher={American Mathematical Society, Providence, RI}, year={2015}, pages={xii+363}, isbn={978-0-8218-5198-2}, } @article {Mas72, AUTHOR = {Mason, J. H.}, TITLE = {Matroids: unimodal conjectures and {M}otzkin's theorem}, BOOKTITLE = {Combinatorics ({P}roc. {C}onf. {C}ombinatorial {M}ath., {M}ath. {I}nst., {O}xford, 1972)}, PAGES = {207--220}, PUBLISHER = {Inst. Math. Appl., Southend-on-Sea}, YEAR = {1972}, MRCLASS = {05B35}, MRNUMBER = {0349445}, MRREVIEWER = {W. Dorfler}, } @article {McM93, AUTHOR = {McMullen, Peter}, TITLE = {On simple polytopes}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {113}, YEAR = {1993}, NUMBER = {2}, PAGES = {419--444}, ISSN = {0020-9910}, MRCLASS = {52B05 (52B35)}, MRNUMBER = {1228132}, MRREVIEWER = {Bernd Kind}, DOI = {10.1007/BF01244313}, } @book {Mur03, AUTHOR = {Murota, Kazuo}, TITLE = {Discrete convex analysis}, SERIES = {SIAM Monographs on Discrete Mathematics and Applications}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA}, YEAR = {2003}, PAGES = {xxii+389}, ISBN = {0-89871-540-7}, MRCLASS = {90-02 (52-02 90C27 90C46 91B02)}, MRNUMBER = {1997998}, MRREVIEWER = {Ulrich Faigle}, DOI = {10.1137/1.9780898718508}, } @book{MS05, author={Meyer, Dagmar M. and Smith, Larry}, title={{Poincar\'{e} duality algebras, Macaulay's dual systems, and Steenrod operations}}, series={Cambridge Tracts in Mathematics}, volume={167}, publisher={Cambridge University Press, Cambridge}, year={2005}, pages={viii+193}, isbn={978-0-521-85064-3}, doi={10.1017/CBO9780511542855}, } @book{MS05b, author={Miller, Ezra and Sturmfels, Bernd}, title={Combinatorial commutative algebra}, year={2005}, series={Graduate Texts in Mathematics}, volume={227}, publisher={Springer-Verlag}, isbn={0-387-23707-0} } @article {Nar95, AUTHOR = {Narayanan, H.}, TITLE = {Convolution and {D}ilworth truncation of submodular functions}, JOURNAL = {J. Indian Inst. Sci.}, FJOURNAL = {Journal of the Indian Institute of Science. A Multidisciplinary Reviews Journal}, VOLUME = {75}, YEAR = {1995}, NUMBER = {1}, PAGES = {25--47}, ISSN = {0970-4140}, MRCLASS = {05B35}, MRNUMBER = {1367194}, } @book{Oxl11, author={Oxley, James}, title={{Matroid theory}}, series={Oxford Graduate Texts in Mathematics}, volume={21}, edition={2}, publisher={Oxford University Press, Oxford}, year={2011}, pages={xiv+684}, isbn={978-0-19-960339-8}, } @article {Pos09, AUTHOR = {Postnikov, Alexander}, TITLE = {Permutohedra, associahedra, and beyond}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2009}, NUMBER = {6}, PAGES = {1026--1106}, ISSN = {1073-7928}, MRCLASS = {05E30}, MRNUMBER = {2487491}, DOI = {10.1093/imrn/rnn153}, } @article {PRW08, AUTHOR = {Postnikov, Alex and Reiner, Victor and Williams, Lauren}, TITLE = {Faces of generalized permutohedra}, JOURNAL = {Doc. Math.}, FJOURNAL = {Documenta Mathematica}, VOLUME = {13}, YEAR = {2008}, PAGES = {207--273}, ISSN = {1431-0635}, MRCLASS = {05E30 (05A15)}, MRNUMBER = {2520477}, } @article{Rot71, Author = {Rota, Gian-Carlo}, Booktitle = {Actes du {C}ongr{\`e}s {I}nternational des {M}ath\'{e}maticiens ({N}ice, 1970), {T}ome 3}, Date-Added = {2019-04-24 15:32:39 +0300}, Date-Modified = {2019-04-24 15:32:39 +0300}, Mrclass = {05B25}, Mrnumber = {0505646}, Pages = {229--233}, Publisher = {Gauthier-Villars, Paris}, Title = {Combinatorial theory, old and new}, Url = {https://mathscinet.ams.org/mathscinet-getitem?mr=0505646}, Year = {1971}, Bdsk-Url-1 = {https://mathscinet.ams.org/mathscinet-getitem?mr=0505646}} @article {Rad42, AUTHOR = {Rado, R.}, TITLE = {A theorem on independence relations}, JOURNAL = {Quart. J. Math., Oxford Ser.}, FJOURNAL = {The Quarterly Journal of Mathematics. Oxford. Second Series}, VOLUME = {13}, YEAR = {1942}, PAGES = {83--89}, ISSN = {0033-5606}, MRCLASS = {27.2X}, MRNUMBER = {0008250}, MRREVIEWER = {L. W. Cohen}, DOI = {10.1093/qmath/os-13.1.83}, } @article{Spe08, author={Speyer, David E.}, title={{Tropical linear spaces}}, journal={SIAM J. Discrete Math.}, volume={22}, year={2008}, number={4}, pages={1527--1558}, issn={0895-4801}, doi={10.1137/080716219}, } @article {Tum99, AUTHOR = {Tuma, Ji\v{r}\'{\i}}, TITLE = {Intersecting matroids by a hyperplane}, JOURNAL = {European J. Combin.}, FJOURNAL = {European Journal of Combinatorics}, VOLUME = {20}, YEAR = {1999}, NUMBER = {5}, PAGES = {445--460}, ISSN = {0195-6698}, MRCLASS = {05B35}, MRNUMBER = {1703182}, DOI = {10.1006/eujc.1999.0288}, } @book{Wel76, Author = {Welsh, D. J. A.}, Date-Added = {2019-04-24 15:34:08 +0300}, Date-Modified = {2019-04-24 15:34:08 +0300}, Mrclass = {05B35}, Mrnumber = {0427112}, Mrreviewer = {W. T. Tutte}, Note = {L. M. S. Monographs, No. 8}, Pages = {xi+433}, Publisher = {Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York}, Title = {Matroid theory}, Url = {https://mathscinet.ams.org/mathscinet-getitem?mr=0427112}, Year = {1976}, Bdsk-Url-1 = {https://mathscinet.ams.org/mathscinet-getitem?mr=0427112}}