Principal Borel ideals and Gotzmann ideals

摘要

In this paper we characterize all principal Borel ideals with Borel generator up to degree 4 which are Gotzmann. We also classify principal Borel ieals with a Borel generator of degree d which are lexsegment and we describe the shadows of principal Borel ideals, Finally, we discuss the corresponding results for squarefree monomial ideals.