Segre Embeddings, Hilbert Series and Newcomb’s Problem
نویسنده
چکیده
Monomial ideals and toric rings are closely related. By consider a Grobner basis we can always associated to any ideal I in a polynomial ring a monomial ideal in≺I, in some special situations the monomial ideal in≺I is square free. On the other hand given any monomial ideal I of a polynomial ring S, we can define the toric K[I] ⊂ S. In this paper we will study toric rings defined by Segre embeddings, we will prove that their h− vectors coincides with the so called Simon Newcomb number’s in probabilities and combinatorics. We can prove by elementary means previous results founded by using probability theory on Markov process. We also get informations about Betti numbers and Mark Green’s invariant for Segre embeddings.
منابع مشابه
Veronese transform, and Castelnuovo-Mumford regularity of modules
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