A numerical property of Hilbert functions and lex segment ideals
J. Korean Math. Soc. 2020 Vol. 57, No. 3, 777-792
https://doi.org/10.4134/JKMS.j190380
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
Downloads: Full-text PDF   Full-text HTML

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd