The algebraic method in tree percolation
- Mohammadi, F. 3
- Sáenz-De-Cabezón, E. 1
- Wynn, H.P. 2
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1
Universidad de La Rioja
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2
London School of Economics and Political Science
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3
Technical University of Berlin
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ISSN: 0895-4801
Any de publicació: 2016
Volum: 30
Número: 2
Pàgines: 1193-1212
Tipus: Article
Altres publicacions en: SIAM Journal on Discrete Mathematics
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Resum
We apply the methods of algebraic reliability to the study of percolation on trees. To a complete k-ary tree Tk,nof depth n we assign a monomial ideal Ik,non ∑n i=1ki variables and kn minimal monomial generators. We give explicit recursive formulae for the Betti numbers of Ik,nand their Hilbert series, which allow us to study explicitly percolation on Tk,n. We study bounds on this percolation and study its asymptotical behavior with the mentioned commutative algebra techniques. © 2016 Society for Industrial and Applied Mathematics.