English

On the oddness of percolation

Statistical Mechanics 2020-09-04 v2

Abstract

Recently Mertens and Moore [arXiv:1909.01484v1] showed that site percolation "is odd." By this they mean that on an M×NM\times N square lattice the number of distinct site configurations that allow for vertical percolation is odd. We report here an alternative proof, based on recursive use of geometric symmetry, for both free and periodic boundary conditions.

Keywords

Cite

@article{arxiv.1909.06172,
  title  = {On the oddness of percolation},
  author = {C. Appert-Rolland and H. J. Hilhorst},
  journal= {arXiv preprint arXiv:1909.06172},
  year   = {2020}
}

Comments

6 pages, 1 figure; discussion of boundary conditions has been extended

R2 v1 2026-06-23T11:14:28.383Z