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The algebraic method in tree percolation

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

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Identification Number: 10.1137/151003647

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
Subjects: Q Science > QA Mathematics
Sets: Departments > Statistics
Date Deposited: 30 Aug 2016 11:44
Last Modified: 27 Sep 2017 09:05
URI: http://eprints.lse.ac.uk/id/eprint/67537

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