The algebraic method in tree percolation

Mohammadi, Fatemeh, Saenz-de-Cabezon, Eduardo and Wynn, Henry P. ORCID: 0000-0002-6448-1080 (2016) The algebraic method in tree percolation. SIAM Journal on Discrete Mathematics, 30 (2). pp. 1193-1212. ISSN 0895-4801

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Abstract

We apply the methods of algebraic reliability to the study of percolation on trees. To a complete $k$-ary tree $T_{k,n}$ of depth $n$ we assign a monomial ideal $I_{k,n}$ on $\sum_{i=1}^n k^i$ variables and $k^n$ minimal monomial generators. We give explicit recursive formulae for the Betti numbers of $I_{k,n}$ and their Hilbert series, which allow us to study explicitly percolation on $T_{k,n}$. We study bounds on this percolation and study its asymptotical behavior with the mentioned commutative algebra techniques.

Item Type:	Article
Official URL:	http://epubs.siam.org/loi/sjdmec
Additional Information:	© 2016 Society for Industrial and Applied Mathematics
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics
Date Deposited:	30 Aug 2016 11:44
Last Modified:	07 Jan 2024 20:03
URI:	http://eprints.lse.ac.uk/id/eprint/67537

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