Subalgebras generated in degree two with minimal Hilbert function

Abstract

What can be said about the subalgebras of the polynomial ring, with minimal or maximal Hilbert function? This question was discussed in a recent paper by M. Boij and A. Conca. In this paper we study the subalgebras generated in degree two with minimal Hilbert function. The problem to determine the generators of these algebras transfers into a combinatorial problem on counting maximal north-east lattice paths inside a shifted Ferrers diagram. We conjecture that the subalgebras generated in degree two with minimal Hilbert function are generated by an initial Lex or RevLex segment.

Gorenstein rings generated by strongly stable sets of quadratic monomials

“…They show that the f i 's should constitute a strongly stable set of monomials, but it is not clear which strongly stable sets that occur. The second author of this paper made a thorough investigation of the case d = 2 [11]. A subring generated by a strongly stable set of quadratic monomials can be realized as a quotient by a polynomial ring and a determinantal ideal.…”