This is an announcement for the paper "Poincar\'{e} type inequalities on the discrete cube and in the CAR algebra" by Limor Ben-Efraim and Francoise Lust-Piquard. Abstract: We prove Lp Poincare inequalities for functions on the discrete cube and their discrete gradient. We thus recover an exponential inequality and the concentration phenomenon for the uniform probability on the cube first obtained by Bobkov and Gotze. Inequalities involving the discrete gradient and powers of the discrete Laplacian are also considered, for the Lp norm or more general ones. Similar results hold true, replacing functions on the cube by elements of the CAR algebra and considering the annihilation operators and the number operator. Archive classification: Functional Analysis Mathematics Subject Classification: 46E39, 46L57, 46L51 The source file(s), poincare-cube-final.tex: 85518 bytes, is(are) stored in gzipped form as 0702233.gz with size 21kb. The corresponding postcript file has gzipped size 182kb. Submitted from: limor_be@cs.huji.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0702233 or http://arXiv.org/abs/math.FA/0702233 or by email in unzipped form by transmitting an empty message with subject line uget 0702233 or in gzipped form by using subject line get 0702233 to: math@arXiv.org.