Segre Product, H-Polynomials, and Castelnuovo-Mumford Regularity
Résumé
The purpose of this paper is to extend the bilinearity of the Segre product that has been proved recently by Ilse Fischer and Martina Kubitzke under some restricted hypotheses. As a consequence, we get some formulas involving Eulerian polynomials and a nice formula that will be used by the first author to solve the Simon Newcomb problem. We apply these results to compute the postulation number of a series and extend partially the results about Castelnuovo-Mumford regularity of the Segre product of polynomial rings of David A. Cox and Evgeny Materov.