We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the Osequences and encode some information about lex segment ideals. Moreover, we introduce numerical functions called fractal functions, and we use them to solve the open problem of the classification of the Hilbert functions of any bigraded algebra.
Favacchio G. (2020). A numerical property of Hilbert functions and lex segment ideals. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 57(3), 777-792 [10.4134/JKMS.j190380].
A numerical property of Hilbert functions and lex segment ideals
Favacchio G.
2020-01-01
Abstract
We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the Osequences and encode some information about lex segment ideals. Moreover, we introduce numerical functions called fractal functions, and we use them to solve the open problem of the classification of the Hilbert functions of any bigraded algebra.
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