Abstract
In this paper, we will show that a classical theorem of topology is, in fact, a combinatorial one, holding in all projective spaces. In the finite case, that is in the case of Galois geometries, this result enables us to obtain many equations between parameters. The easier ones, relating to the complete cell decomposition of Grassmann varieties, are the classical identities introduced by Sylvester in the study of the theory of the partitions. So we start by recalling the Sylvester equality; in Section 2 we shall define Schubert cells and related theorems in the abstract case; finally, in Section 3 we shall consider Galois projective spaces.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
