JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org..

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. This study focuses on the impact of sex, race, and social networks, to analyze the hiring process in a midsized high-technology organization, using information on all 35,229 applicants in a 10-year period . For gender, the process is entirely meritocratic: age and education account for all sex differences. But even without taking into account the two meritocratic variables, there are small if no differences between men and women at all stages in the hiring process. For ethnic minorities, the process is partly meritocratic but partly reliant upon social networks. Once referral method is taken into account, all race effects disappear. In hiring, ethnic minorities are thus disadvantaged in the processes that take place before the organization is contacted. They lack access to or utilize less well the social networks that lead to high success in getting hired.

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We present examples of flag homology spheres whose γ -vectors satisfy the Kruskal-Katona inequalities. This includes several families of well-studied simplicial complexes, including Coxeter complexes and the simplicial complexes dual to the associahedron and to the cyclohedron. In these cases, we construct explicit flag simplicial complexes whose f -vectors are the γ -vectors in question, and so a result of Frohmader shows that the γ -vectors satisfy not only the Kruskal-Katona inequalities but also the stronger Frankl-Füredi-Kalai inequalities. In another direction, we show that if a flag (d − 1)-sphere has at most 2d + 3 vertices its γ -vector satisfies the Frankl-Füredi-Kalai inequalities. We conjecture that if Δ is a flag homology sphere then γ (Δ) satisfies the Kruskal-Katona, and further, the Frankl-Füredi-Kalai inequalities. This conjecture is a significant refinement of Gal's conjecture, which asserts that such γ -vectors are nonnegative.

We show that Schützenberger's promotion on two and three row rectangular Young tableaux can be realized as cyclic rotation of certain planar graphs introduced by Kuperberg. Moreover, following work of the third author, we show that this action admits the cyclic sieving phenomenon.