@misc{AKNarxiv, Author = {Adin, R.M. and Kalmanovich, D. and Nevo, E.}, Eprint = {1801.00163}, Eprinttype = {arxiv}, Title = {On the cone of $f$-vectors of cubical polytopes}, Year = {\textit{Proc. Amer. Math. Soc.} (to appear)}, } @article {Barn73, AUTHOR = {Barnette, D.}, TITLE = {A proof of the lower bound conjecture for convex polytopes}, JOURNAL = {Pacific J. Math.}, FJOURNAL = {Pacific Journal of Mathematics}, VOLUME = {46}, YEAR = {1973}, PAGES = {349--354}, MRCLASS = {52A25}, MRNUMBER = {0328773}, MRREVIEWER = {E. Jucovic}, URL = {http://projecteuclid.org/euclid.pjm/1102946311}, } @article {BlinB95, AUTHOR = {Blind, G. and Blind, R.}, TITLE = {The cubical {$d$}-polytopes with fewer than {$2^{d+1}$} vertices}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {13}, YEAR = {1995}, NUMBER = {3-4}, PAGES = {321--345}, MRCLASS = {52B05}, MRNUMBER = {1318781}, MRREVIEWER = {Margaret M. Bayer}, DOI = {10.1007/BF02574048}, } @article {Jock93, AUTHOR = {Jockusch, W.}, TITLE = {The lower and upper bound problems for cubical polytopes}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {9}, YEAR = {1993}, NUMBER = {2}, PAGES = {159--163}, CODEN = {DCGEER}, MRCLASS = {52B05}, MRNUMBER = {1194033 (93j:52016)}, MRREVIEWER = {Margaret M. Bayer}, DOI = {10.1007/BF02189315}, } @article {nevo_VKobs, AUTHOR = {Nevo, E.}, TITLE = {Higher minors and {V}an {K}ampen's obstruction}, JOURNAL = {Math. Scand.}, FJOURNAL = {Mathematica Scandinavica}, VOLUME = {101}, YEAR = {2007}, NUMBER = {2}, PAGES = {161--176}, MRCLASS = {55U10 (05C83 55S35)}, MRNUMBER = {2379282}, MRREVIEWER = {Paul G. Goerss}, DOI = {10.7146/math.scand.a-15037}, } @article {Klee11, AUTHOR = {Klee, S.}, TITLE = {Lower bounds for cubical pseudomanifolds}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {46}, YEAR = {2011}, NUMBER = {2}, PAGES = {212--222}, MRCLASS = {52B70 (05A15 05E45)}, MRNUMBER = {2812506}, MRREVIEWER = {Satyan L. Devadoss}, DOI = {10.1007/s00454-011-9329-9}, } @incollection {Kalai:missing, AUTHOR = {Kalai, G.}, TITLE = {Some aspects of the combinatorial theory of convex polytopes}, BOOKTITLE = {Polytopes: abstract, convex and computational ({S}carborough, {ON}, 1993)}, SERIES = {NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.}, VOLUME = {440}, PAGES = {205--229}, PUBLISHER = {Kluwer Acad. Publ., Dordrecht}, YEAR = {1994}, MRCLASS = {52B05 (52B11)}, MRNUMBER = {1322063}, MRREVIEWER = {P. McMullen}, } @article {Nagel:missing, AUTHOR = {Nagel, U.}, TITLE = {Empty simplices of polytopes and graded {B}etti numbers}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {39}, YEAR = {2008}, NUMBER = {1--3}, PAGES = {389--410}, MRCLASS = {52B70 (13F55)}, MRNUMBER = {2383766}, MRREVIEWER = {Enrique Reyes}, DOI = {10.1007/s00454-008-9057-y}, } @article {Bagchi-Datta, AUTHOR = {Bagchi, B. and Datta, B.}, TITLE = {On {$k$}-stellated and {$k$}-stacked spheres}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {313}, YEAR = {2013}, NUMBER = {20}, PAGES = {2318--2329}, MRCLASS = {57Qxx (55U10)}, MRNUMBER = {3084278}, MRREVIEWER = {Jonathan Ariel Barmak}, DOI = {10.1016/j.disc.2013.06.010}, } @unpublished{Sany05, author={Sanyal, R.}, title={On the Combinatorics of Projected Deformed Products}, note={Diploma Thesis, available online at \url{http://page.mi.fu-berlin.de/sanyal/DiplomaThesis.pdf}}, year={2005}, } @article {Stan80, AUTHOR = {Stanley, R.P.}, TITLE = {The number of faces of a simplicial convex polytope}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {35}, YEAR = {1980}, NUMBER = {3}, PAGES = {236--238}, MRCLASS = {52A25 (05B99 14M99)}, MRNUMBER = {563925}, MRREVIEWER = {I. Dolgachev}, DOI = {10.1016/0001-8708(80)90050-X}, } @article {BillL81, AUTHOR = {Billera, L.J. and Lee, C.W.}, TITLE = {A proof of the sufficiency of {M}c{M}ullen's conditions for {$f$}-vectors of simplicial convex polytopes}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {31}, YEAR = {1981}, NUMBER = {3}, PAGES = {237--255}, MRCLASS = {52A25}, MRNUMBER = {635368}, MRREVIEWER = {Udo Pachner}, DOI = {10.1016/0097-3165(81)90058-3}, } @article {McMu71, AUTHOR = {McMullen, P.}, TITLE = {The numbers of faces of simplicial polytopes}, JOURNAL = {Israel J. Math.}, FJOURNAL = {Israel Journal of Mathematics}, VOLUME = {9}, YEAR = {1971}, PAGES = {559--570}, MRCLASS = {52.10}, MRNUMBER = {0278183}, MRREVIEWER = {J. Zaks}, DOI = {10.1007/BF02771471}, } @article {JoswZ00, AUTHOR = {Joswig, M. and Ziegler, G.M.}, TITLE = {Neighborly cubical polytopes}, NOTE = {The Branko Gr\"unbaum birthday issue}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {24}, YEAR = {2000}, NUMBER = {2--3}, PAGES = {325--344}, MRCLASS = {52B05 (52B40)}, MRNUMBER = {1758054}, DOI = {10.1007/s004540010039}, } @inproceedings{Adin96, AUTHOR = {Adin, R.M.}, TITLE = {A new cubical {$h$}-vector}, BOOKTITLE = {Proceedings of the 6th {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({N}ew {B}runswick, {NJ}, 1994)}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {157}, YEAR = {1996}, NUMBER = {1-3}, PAGES = {3--14}, CODEN = {DSMHA4}, MRCLASS = {52B05}, MRNUMBER = {1417283}, MRREVIEWER = {P. McMullen}, DOI = {10.1016/S0012-365X(96)83003-2}, } @article {BabsBC97, AUTHOR = {Babson, E.K. and Billera, L.J. and Chan, C.S.}, TITLE = {Neighborly cubical spheres and a cubical lower bound conjecture}, JOURNAL = {Israel J. Math.}, FJOURNAL = {Israel Journal of Mathematics}, VOLUME = {102}, YEAR = {1997}, PAGES = {297--315}, CODEN = {ISJMAP}, MRCLASS = {52B12}, MRNUMBER = {1489110}, MRREVIEWER = {P. McMullen}, DOI = {10.1007/BF02773804}, } @article {SanyZ10, AUTHOR = {Sanyal, R. and Ziegler, G.M.}, TITLE = {Construction and analysis of projected deformed products}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {43}, YEAR = {2010}, NUMBER = {2}, PAGES = {412--435}, CODEN = {DCGEER}, MRCLASS = {52A20}, MRNUMBER = {2579706}, MRREVIEWER = {Enrique Reyes}, DOI = {10.1007/s00454-009-9146-6}, } @article {McMuW71, AUTHOR = {McMullen, P. and Walkup, D.W.}, TITLE = {A generalized lower-bound conjecture for simplicial polytopes}, JOURNAL = {Mathematika}, FJOURNAL = {Mathematika. A Journal of Pure and Applied Mathematics}, VOLUME = {18}, YEAR = {1971}, PAGES = {264--273}, MRCLASS = {52A40}, MRNUMBER = {0298557}, MRREVIEWER = {D. Barnette}, } @unpublished{KaibW03, author = {Kaibel, V. and Wassmer, A.}, title = {Automorphism Groups of Cyclic Polytopes}, year = {2003}, note = {available at \url{http://www.math.uni-magdeburg.de/~kaibel/Downloads/LocalPapers/KaibelW03.pdf}}, } @article {Shep68, AUTHOR = {Shephard, G.~C.}, TITLE = {A theorem on cyclic polytopes}, JOURNAL = {Israel J. Math.}, FJOURNAL = {Israel Journal of Mathematics}, VOLUME = {6}, YEAR = {1968}, PAGES = {368--372 (1969)}, MRCLASS = {52.10}, MRNUMBER = {0244856}, MRREVIEWER = {G. T. Sallee}, } @book {Zieg95, AUTHOR = {Ziegler, G.M.}, TITLE = {Lectures on polytopes}, SERIES = {Graduate Texts in Mathematics}, VOLUME = {152}, PUBLISHER = {Springer-Verlag, New York}, YEAR = {1995}, PAGES = {x+370}, MRCLASS = {52Bxx}, MRNUMBER = {1311028}, MRREVIEWER = {Margaret M. Bayer}, DOI = {10.1007/978-1-4613-8431-1}, } @article {MuraN13, AUTHOR = {Murai, S. and Nevo, E.}, TITLE = {On the generalized lower bound conjecture for polytopes and spheres}, JOURNAL = {Acta Math.}, FJOURNAL = {Acta Mathematica}, VOLUME = {210}, YEAR = {2013}, NUMBER = {1}, PAGES = {185--202}, MRCLASS = {52B05 (05Bxx)}, MRNUMBER = {3037614}, MRREVIEWER = {Benjamin Braun}, DOI = {10.1007/s11511-013-0093-y}, }