A numerical property of Hilbert functions and lex segment ideals
J. Korean Math. Soc. 2020 Vol. 57, No. 3, 777-792
Published online May 1, 2020
Giuseppe Favacchio
Universit\`a degli Studi di Catania
Abstract : We introduce the \textit{fractal expansions}, sequences of integers associated to a number. We show that these sequences characterize the $O$-sequences and encode some information about lex segment ideals. Moreover, we introduce numerical functions called \textit{fractal functions}, and we use them to solve the open problem of the classification of the Hilbert functions of any bigraded algebra.
Keywords : Hilbert function, lex segment ideal, bigraded algebra
MSC numbers : Primary 13F20, 13A15, 13D40
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