E. Babson and E. Nevo, Lefschetz properties and basic constructions on??simplicial spheres, Journal of Algebraic Combinatorics, vol.16, issue.4, 2008.
DOI : 10.1007/s10801-009-0189-9

URL : http://arxiv.org/abs/0802.1058

E. Babson, I. Novik, and R. Thomas, Reverse lexicographic and lexicographic shifting, Journal of Algebraic Combinatorics, vol.40, issue.2, pp.107-123, 2006.
DOI : 10.1007/s10801-006-6919-3

URL : http://arxiv.org/abs/math/0507565

L. J. Billera and C. W. Lee, A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes, Journal of Combinatorial Theory, Series A, vol.31, issue.3, pp.237-255, 1981.
DOI : 10.1016/0097-3165(81)90058-3

A. Björner and G. Kalai, On f-Vectors and Homology, Combinatorial Mathematics: Proc. 3rd Intern. Conf, pp.63-80, 1985.
DOI : 10.1007/BF01229745

T. K. Dey, H. Edelsbrunner, S. Guha, and D. V. Nekhayev, Topology preserving edge contraction, Publ. Inst. Math. (Beograd) (N.S.), vol.66, issue.80, pp.23-45, 1999.

D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Grad. Texts in Math, vol.150, 1995.

P. Erdös, C. Ko, and R. Rado, INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS, The Quarterly Journal of Mathematics, vol.12, issue.1, pp.313-320, 1961.
DOI : 10.1093/qmath/12.1.313

J. Herzog, Generic initial ideals and graded Betti numbers, Computational commutative algebra and combinatorics, pp.75-120, 2002.

G. Kalai, Characterization off-vectors of families of convex sets inR d Part I: Necessity of Eckhoff???s conditions, Israel Journal of Mathematics, vol.26, issue.2-3, pp.175-195, 1984.
DOI : 10.1007/BF02761163

G. Kalai, Many triangulated spheres, Discrete & Computational Geometry, vol.28, issue.1, pp.1-14, 1988.
DOI : 10.1007/BF02187893

G. Kalai, The diameter of graphs of convex polytopes and f -vector theory Applied geometry and discrete mathematics, DIMACS Ser. Discrete Math. Theoret. Comput. Sci, vol.4, pp.387-411, 1991.

G. Kalai, Algebraic shifting Computational commutative algebra and combinatorics, Adv. Stud. Pure Math. Math. Soc. Japan, vol.33, pp.121-163, 2002.

S. Murai, Algebraic shifting of cyclic polytopes and stacked polytopes. Discrete Math, pp.1707-1721, 2007.

S. Murai, Generic initial ideals and squeezed spheres, Advances in Mathematics, vol.214, issue.2, pp.701-729, 2007.
DOI : 10.1016/j.aim.2007.03.004

S. Murai, Algebraic shifting of strongly edge decomposable spheres, Journal of Combinatorial Theory, Series A, vol.117, issue.1, 2008.
DOI : 10.1016/j.jcta.2009.04.002

S. Murai and T. Hibi, Algebraic shifting and graded Betti numbers, Transactions of the American Mathematical Society, vol.361, issue.04, 2005.
DOI : 10.1090/S0002-9947-08-04707-7

E. Nevo, Algebraic Shifting and Basic Constructions on Simplicial Complexes, Journal of Algebraic Combinatorics, vol.33, issue.4, pp.411-433, 2005.
DOI : 10.1007/s10801-005-4626-0

URL : http://arxiv.org/abs/math/0303233

E. Nevo, Higher minors and Van Kampen's obstruction. arXive:math.CO/0602531, Math. Scand, 2006.
DOI : 10.7146/math.scand.a-15037

URL : http://arxiv.org/abs/math/0602531

R. P. Stanley, The number of faces of a simplicial convex polytope, Advances in Mathematics, vol.35, issue.3, pp.236-238, 1980.
DOI : 10.1016/0001-8708(80)90050-X

R. P. Stanley, Combinatorics and commutative algebra, Progr. Math, vol.41, 1996.
DOI : 10.1007/978-1-4899-6752-7