%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% My papers %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @misc{sagemath, Key = {SageMath}, Author = {{The Sage Developers}}, Title = {{S}ageMath, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion x.y.z)}, note={\url{https://www.sagemath.org}}, } @book {ec2, AUTHOR = {Stanley, Richard P.}, TITLE = {Enumerative combinatorics. {V}ol. 2}, SERIES = {Cambridge Studies in Advanced Mathematics}, VOLUME = {62}, NOTE = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {1999}, PAGES = {xii+581}, ISBN = {0-521-56069-1; 0-521-78987-7}, MRCLASS = {05A15 (05-02 05E05 05E10 68R05)}, MRNUMBER = {1676282}, MRREVIEWER = {Ira Gessel}, DOI = {10.1017/CBO9780511609589}, opturl = {https://doi.org/10.1017/CBO9780511609589}, } @article {bvoriginal, AUTHOR = {Berline, Nicole and Vergne, Mich\`ele}, TITLE = {Local {E}uler-{M}aclaurin formula for polytopes}, JOURNAL = {Mosc. Math. J.}, FJOURNAL = {Moscow Mathematical Journal}, VOLUME = {7}, YEAR = {2007}, NUMBER = {3}, PAGES = {355--386, 573}, ISSN = {1609-3321}, MRCLASS = {52B20}, MRNUMBER = {2343137}, MRREVIEWER = {P. McMullen}, DOI = {10.17323/1609-4514-2007-7-3-355-386}, opturl = {https://doi.org/10.17323/1609-4514-2007-7-3-355-386}, } @article {nill, AUTHOR = {Castillo, Federico and Liu, Fu and Nill, Benjamin and Paffenholz, Andreas}, TITLE = {Smooth polytopes with negative {E}hrhart coefficients}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {160}, YEAR = {2018}, PAGES = {316--331}, ISSN = {0097-3165}, MRCLASS = {52B20}, MRNUMBER = {3846206}, MRREVIEWER = {Robert Davis}, DOI = {10.1016/j.jcta.2018.06.014}, opturl = {https://doi.org/10.1016/j.jcta.2018.06.014}, } @incollection {positivesurvey, AUTHOR = {Liu, Fu}, TITLE = {On positivity of {E}hrhart polynomials}, BOOKTITLE = {Recent trends in algebraic combinatorics}, SERIES = {Assoc. Women Math. Ser.}, VOLUME = {16}, PAGES = {189--237}, PUBLISHER = {Springer, Cham}, YEAR = {2019}, MRCLASS = {05E05 (05E45 52B20)}, MRNUMBER = {3969575}, } @book {barvinokconvex, AUTHOR = {Barvinok, Alexander}, TITLE = {A course in convexity}, SERIES = {Graduate Studies in Mathematics}, VOLUME = {54}, PUBLISHER = {American Mathematical Society, Providence, RI}, YEAR = {2002}, PAGES = {x+366}, ISBN = {0-8218-2968-8}, MRCLASS = {52-02 (49N15 52-01 90-02 90C05 90C22 90C25)}, MRNUMBER = {1940576}, MRREVIEWER = {P. McMullen}, DOI = {10.1090/gsm/054}, opturl = {http://dx.doi.org/10.1090/gsm/054}, } @article {matroidpolytope, AUTHOR = {Ardila, Federico and Benedetti, Carolina and Doker, Jeffrey}, TITLE = {Matroid polytopes and their volumes}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {43}, YEAR = {2010}, NUMBER = {4}, PAGES = {841--854}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {52B40 (05B35)}, MRNUMBER = {2610473 (2012b:52026)}, MRREVIEWER = {Sonoko Moriyama}, DOI = {10.1007/s00454-009-9232-9}, opturl = {http://dx.doi.org/10.1007/s00454-009-9232-9}, } @article {faces, 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 (2010j:05425)}, } @article {bible, 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 (2010g:05399)}, DOI = {10.1093/imrn/rnn153}, opturl = {http://dx.doi.org/10.1093/imrn/rnn153}, } @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}, MRCLASS = {05-02 (05A15 06-02)}, MRNUMBER = {2868112}, } @article {ranktest, AUTHOR = {Morton, Jason and Pachter, Lior and Shiu, Anne and Sturmfels, Bernd and Wienand, Oliver}, TITLE = {Convex rank tests and semigraphoids}, JOURNAL = {SIAM J. Discrete Math.}, FJOURNAL = {SIAM Journal on Discrete Mathematics}, VOLUME = {23}, YEAR = {2009}, NUMBER = {3}, PAGES = {1117--1134}, ISSN = {0895-4801}, MRCLASS = {62G10 (52B05)}, MRNUMBER = {2538642 (2011b:62126)}, MRREVIEWER = {Ruriko Yoshida}, DOI = {10.1137/080715822}, opturl = {http://dx.doi.org/10.1137/080715822}, } @article {highintegral, AUTHOR = {Liu, Fu}, TITLE = {Higher integrality conditions, volumes and {E}hrhart polynomials}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {226}, YEAR = {2011}, NUMBER = {4}, PAGES = {3467--3494}, ISSN = {0001-8708}, CODEN = {ADMTA4}, MRCLASS = {52B20 (05A15 52A38)}, MRNUMBER = {2764894 (2012a:52031)}, MRREVIEWER = {Ruriko Yoshida}, DOI = {10.1016/j.aim.2010.10.023}, opturl = {http://dx.doi.org/10.1016/j.aim.2010.10.023}, } @misc{casliu-BValpha-v1, AUTHOR = {Castillo, Federico and Liu, Fu}, TITLE = {Berline-Vergne valuation and generalized permutohedra}, YEAR = {2015}, eprint={1509.07884v1}, } @misc{kat, AUTHOR = {Jochemko, Katharina and Ravichandran, Mohan}, TITLE = {Generalized permutahedra: Minkowski linear functionals and Ehrhart positivity}, YEAR = {2019}, eprint={1909.08448}, } @article {bvalpha, AUTHOR = {Castillo, Federico and Liu, Fu}, TITLE = {Berline-{V}ergne valuation and generalized permutohedra}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {60}, YEAR = {2018}, NUMBER = {4}, PAGES = {885--908}, ISSN = {0179-5376}, MRCLASS = {52B20 (52B45 90C57)}, MRNUMBER = {3869454}, MRREVIEWER = {Robert Davis}, DOI = {10.1007/s00454-017-9950-3}, opturl = {https://doi.org/10.1007/s00454-017-9950-3}, } @book {barvinok, AUTHOR = {Barvinok, Alexander}, TITLE = {Integer points in polyhedra}, SERIES = {Zurich Lectures in Advanced Mathematics}, PUBLISHER = {European Mathematical Society (EMS), Z\"urich}, YEAR = {2008}, PAGES = {viii+191}, ISBN = {978-3-03719-052-4}, MRCLASS = {52-02 (05-02 05A15 11H06 52B20 52B45 52B55 52C07 52C45)}, MRNUMBER = {2455889 (2011a:52001)}, MRREVIEWER = {Martin Henk}, DOI = {10.4171/052}, opturl = {http://dx.doi.org/10.4171/052}, } @article {localformula, AUTHOR = {Berline, Nicole and Vergne, Mich{\`e}le}, TITLE = {Local {E}uler-{M}aclaurin formula for polytopes}, JOURNAL = {Mosc. Math. J.}, FJOURNAL = {Moscow Mathematical Journal}, VOLUME = {7}, YEAR = {2007}, NUMBER = {3}, PAGES = {355--386, 573}, ISSN = {1609-3321}, MRCLASS = {52B20}, MRNUMBER = {2343137 (2008k:52026)}, MRREVIEWER = {P. McMullen}, } @ARTICLE{danilov, author = {V.I. Danilov}, title = {The geometry of toric varieties}, journal = {Russian Math. Surveys}, volume = 33, number = 2, year = 1978, pages = "97--154", } @article {mcmullen, AUTHOR = {McMullen, P.}, TITLE = {Valuations and {E}uler-type relations on certain classes of convex polytopes}, JOURNAL = {Proc. London Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {35}, YEAR = {1977}, NUMBER = {1}, PAGES = {113--135}, ISSN = {0024-6115}, MRCLASS = {52A25}, MRNUMBER = {0448239 (56 \#6548)}, MRREVIEWER = {P. R. Goodey}, } @incollection {mcmullenext, AUTHOR = {McMullen, Peter}, TITLE = {Valuations and dissections}, BOOKTITLE = {Handbook of convex geometry, {V}ol. {A}, {B}}, PAGES = {933--988}, PUBLISHER = {North-Holland, Amsterdam}, YEAR = {1993}, MRCLASS = {52B45}, MRNUMBER = {1243000}, MRREVIEWER = {B. Kind}, } @ARTICLE{morelli, author = {Morelli, Robert}, title = {Pick's theorem and the {T}odd class of a toric variety}, journal = {Adv. Math.}, fjournal = {Advances in Mathematics}, volume = 100, number = 2, year = 1993, pages = "183--231", doi = {10.1006/aima.1993.1033}, } @article {perturbation, AUTHOR = {Liu, Fu}, TITLE = {Perturbation of transportation polytopes}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {120}, YEAR = {2013}, NUMBER = {7}, PAGES = {1539--1561}, ISSN = {0097-3165}, MRCLASS = {52B12 (05A15 52B11)}, MRNUMBER = {3092682}, MRREVIEWER = {Ragnar Freij}, DOI = {10.1016/j.jcta.2013.05.003}, opturl = {http://dx.doi.org/10.1016/j.jcta.2013.05.003}, } @article {toddclass, AUTHOR = {Pommersheim, James and Thomas, Hugh}, TITLE = {Cycles representing the {T}odd class of a toric variety}, JOURNAL = {J. Amer. Math. Soc.}, FJOURNAL = {Journal of the American Mathematical Society}, VOLUME = {17}, YEAR = {2004}, NUMBER = {4}, PAGES = {983--994}, ISSN = {0894-0347}, MRCLASS = {14M25 (14C17 52B20)}, MRNUMBER = {2083474 (2005h:14124)}, MRREVIEWER = {Dimitrios I. Dais}, DOI = {10.1090/S0894-0347-04-00460-6}, opturl = {http://dx.doi.org/10.1090/S0894-0347-04-00460-6}, } @preamble{ "\def\cprime{$'$} " } @article {GGMS, AUTHOR = {Gel{\cprime}fand, I. M. and Goresky, R. M. and MacPherson, R. D. and Serganova, V. V.}, TITLE = {Combinatorial geometries, convex polyhedra, and {S}chubert cells}, JOURNAL = {Adv. in Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {63}, YEAR = {1987}, NUMBER = {3}, PAGES = {301--316}, ISSN = {0001-8708}, CODEN = {ADMTA4}, MRCLASS = {14M15 (05B35 22E45 22E70 32C38 32C45 32M10)}, MRNUMBER = {877789 (88f:14045)}, MRREVIEWER = {Hiroaki Terao}, DOI = {10.1016/0001-8708(87)90059-4}, opturl = {http://dx.doi.org/10.1016/0001-8708(87)90059-4}, } @article {deloera, AUTHOR = {De Loera, Jes{\'u}s A. and Haws, David C. and K{\"o}ppe, Matthias}, TITLE = {Ehrhart polynomials of matroid polytopes and polymatroids}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {42}, YEAR = {2009}, NUMBER = {4}, PAGES = {670--702}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {52B40 (05B35)}, MRNUMBER = {2556462 (2011b:52015)}, MRREVIEWER = {Jakayla R. Robbins}, DOI = {10.1007/s00454-008-9080-z}, opturl = {http://dx.doi.org/10.1007/s00454-008-9080-z}, } @incollection {zonotopes, AUTHOR = {Stanley, Richard P.}, TITLE = {A zonotope associated with graphical degree sequences}, BOOKTITLE = {Applied geometry and discrete mathematics}, SERIES = {DIMACS Ser. Discrete Math. Theoret. Comput. Sci.}, VOLUME = {4}, PAGES = {555--570}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {1991}, MRCLASS = {52B20 (05C30 52B05)}, MRNUMBER = {1116376 (92k:52020)}, MRREVIEWER = {P. McMullen}, } @article {stanley-pitman, AUTHOR = {Stanley, Richard P. and Pitman, Jim}, TITLE = {A polytope related to empirical distributions, plane trees, parking functions, and the associahedron}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {27}, YEAR = {2002}, NUMBER = {4}, PAGES = {603--634}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {52B11 (05A15 60C05)}, MRNUMBER = {1902680 (2003e:52017)}, MRREVIEWER = {Igor Rivin}, DOI = {10.1007/s00454-002-2776-6}, opturl = {http://dx.doi.org/10.1007/s00454-002-2776-6}, } @article {cyclic, AUTHOR = {Liu, Fu}, TITLE = {Ehrhart polynomials of cyclic polytopes}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {111}, YEAR = {2005}, NUMBER = {1}, PAGES = {111--127}, ISSN = {0097-3165}, CODEN = {JCBTA7}, MRCLASS = {05A15 (52B05)}, MRNUMBER = {2144858 (2006a:05012)}, MRREVIEWER = {Matthias Beck}, DOI = {10.1016/j.jcta.2004.11.011}, opturl = {http://dx.doi.org/10.1016/j.jcta.2004.11.011}, } @article {rado, AUTHOR = {Rado, R.}, TITLE = {An inequality}, JOURNAL = {J. London Math. Soc.}, FJOURNAL = {Journal of the London Mathematical Society. Second Series}, VOLUME = {27}, YEAR = {1952}, PAGES = {1--6}, ISSN = {0024-6107}, MRCLASS = {27.0X}, MRNUMBER = {0045168 (13,539e)}, MRREVIEWER = {R. C. Lyndon}, } @book {schrijver, AUTHOR = {Schrijver, Alexander}, TITLE = {Combinatorial optimization. {P}olyhedra and efficiency. {V}ol. {B}}, SERIES = {Algorithms and Combinatorics}, VOLUME = {24}, NOTE = {Matroids, trees, stable sets, Chapters 39--69}, 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 (2004b:90004b)}, MRREVIEWER = {Alexander I. Barvinok}, } @article {mcmullen, AUTHOR = {McMullen, P.}, TITLE = {Valuations and {E}uler-type relations on certain classes of convex polytopes}, JOURNAL = {Proc. London Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {35}, YEAR = {1977}, NUMBER = {1}, PAGES = {113--135}, ISSN = {0024-6115}, MRCLASS = {52A25}, MRNUMBER = {0448239 (56 \#6548)}, MRREVIEWER = {P. R. Goodey}, } @book {ewald, AUTHOR = {Ewald, G{\"u}nter}, TITLE = {Combinatorial convexity and algebraic geometry}, SERIES = {Graduate Texts in Mathematics}, VOLUME = {168}, PUBLISHER = {Springer-Verlag, New York}, YEAR = {1996}, PAGES = {xiv+372}, ISBN = {0-387-94755-8}, MRCLASS = {52B20 (14M25 52B05)}, MRNUMBER = {1418400 (97i:52012)}, MRREVIEWER = {P. McMullen}, DOI = {10.1007/978-1-4612-4044-0}, opturl = {http://dx.doi.org/10.1007/978-1-4612-4044-0}, } @book {enum, 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}, MRCLASS = {05-02 (05A15 06-02)}, MRNUMBER = {2868112}, } @incollection {BarviPom, AUTHOR = {Barvinok, Alexander and Pommersheim, James E.}, TITLE = {An algorithmic theory of lattice points in polyhedra}, BOOKTITLE = {New perspectives in algebraic combinatorics ({B}erkeley, {CA}, 1996--97)}, SERIES = {Math. Sci. Res. Inst. Publ.}, VOLUME = {38}, PAGES = {91--147}, PUBLISHER = {Cambridge Univ. Press, Cambridge}, YEAR = {1999}, MRCLASS = {52C07 (05A15)}, MRNUMBER = {1731815 (2000k:52014)}, } @book {fulton, 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}, MRCLASS = {14M25 (14-02 14J30)}, MRNUMBER = {1234037 (94g:14028)}, MRREVIEWER = {T. Oda}, } @article {intersection, 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}, CODEN = {TPLGAF}, MRCLASS = {14M25 (14C17 52B20)}, MRNUMBER = {1415592 (97h:14070)}, MRREVIEWER = {Michel Brion}, DOI = {10.1016/0040-9383(96)00016-X}, opturl = {http://dx.doi.org/10.1016/0040-9383(96)00016-X}, } @article {gaku, AUTHOR = {Liu, Gaku}, TITLE = {Mixed volumes of hypersimplices}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {23}, YEAR = {2016}, NUMBER = {3}, PAGES = {Paper 3.19, 19}, MRCLASS = {52A39 (05A10)}, MRNUMBER = {3558056}, MRREVIEWER = {Weidong Wang}, } @misc {thesis, AUTHOR = {Castillo, Federico}, TITLE = {Local {E}hrhart Positivity.}, note = {PhD thesis, UC Davis.}, } @article {smooth, AUTHOR = {Castillo, Federico and Liu, Fu and Nill, Benjamin and Paffenholz, Andreas}, TITLE = {Smooth polytopes with negative {E}hrhart coefficients}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {160}, YEAR = {2018}, PAGES = {316--331}, ISSN = {0097-3165}, MRCLASS = {52B20}, MRNUMBER = {3846206}, MRREVIEWER = {Robert Davis}, DOI = {10.1016/j.jcta.2018.06.014}, opturl = {https://doi.org/10.1016/j.jcta.2018.06.014}, } @book {zie, AUTHOR = {Ziegler, G{\"u}nter M.}, TITLE = {Lectures on polytopes}, SERIES = {Graduate Texts in Mathematics}, VOLUME = {152}, PUBLISHER = {Springer-Verlag, New York}, YEAR = {1995}, PAGES = {x+370}, ISBN = {0-387-94365-X}, MRCLASS = {52Bxx}, MRNUMBER = {1311028 (96a:52011)}, MRREVIEWER = {Margaret M. Bayer}, DOI = {10.1007/978-1-4613-8431-1}, opturl = {http://dx.doi.org/10.1007/978-1-4613-8431-1}, } @article {truemcmullen, AUTHOR = {McMullen, Peter}, TITLE = {Weakly continuous valuations on convex polytopes}, JOURNAL = {Arch. Math. (Basel)}, FJOURNAL = {Archiv der Mathematik}, VOLUME = {41}, YEAR = {1983}, NUMBER = {6}, PAGES = {555--564}, ISSN = {0003-889X}, MRCLASS = {52A25 (52A22)}, MRNUMBER = {731639}, MRREVIEWER = {Udo Pachner}, DOI = {10.1007/BF01198585}, opturl = {https://doi.org/10.1007/BF01198585}, }