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Browsing by Author Weiss, Arthur Jay

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  • Authors: Weiss, Arthur Jay (2006)

    In 2005, building on his own recent work and that of F. Zanello, A. Iarrobino discovered some constructions that, he conjectured, would yield level algebras with non-unimodal Hilbert functions. This thesis provides proofs of nonunimodality for Iarrobino’s level algebras, as well as for other level algebras that the author has constructed along similar lines. The key technical contribution is to extend some results published by Iarrobino in 1984. Iarrobino’s results provide insight into some naturally arising vector subspaces of the vector space Rd of forms of fixed degree in a polynomial ring in several variables. In this thesis, the problem is approached by combinatorial methods a...