Abstract. In this paper we characterize all principal Borel ideals with Borel <a class="inlineAdmedialink" href="#">generator</a> up to degree 4 which are Gotzmann. We also classify principal Borel ideals 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.
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