Percolation is Odd

• Published in 2019
• Added on 2019-09-14

We discuss the number of spanning configurations in site percolation. We show that for a large class of lattices, the number of spanning configrations is odd for all lattice sizes. This class includes site percolation on the square lattice and on the hypercubic lattice in any dimension.

Links

• http://arxiv.org/abs/1909.01484v1
• http://arxiv.org/pdf/1909.01484v1

BibTeX entry

@article{PercolationisOdd,
	title = {Percolation is Odd},
	abstract = {We discuss the number of spanning configurations in site percolation. We show
that for a large class of lattices, the number of spanning configrations is odd
for all lattice sizes. This class includes site percolation on the square
lattice and on the hypercubic lattice in any dimension.},
	url = {http://arxiv.org/abs/1909.01484v1 http://arxiv.org/pdf/1909.01484v1},
	year = 2019,
	author = {Stephan Mertens and Cristopher Moore},
	comment = {},
	urldate = {2019-09-14},
	archivePrefix = {arXiv},
	eprint = {1909.01484},
	primaryClass = {cond-mat.stat-mech},
	collections = {Attention-grabbing titles,Combinatorics}
}