Determinants of grids, tori, cylinders and M\"{o}bius ladders
Combinatorics
2012-12-20 v1
Abstract
Recently, Bie\~{n} [A. Bie\~{n}, The problem of singularity for planar grids, Discrete Math. 311 (2011), 921--931] obtained a recursive formula for the determinant of a grid. Also, recently, Pragel [D. Pragel, Determinants of box products of paths, Discrete Math. 312 (2012), 1844--1847], independently, obtained an explicit formula for this determinant. In this paper, we give a short proof for this problem. Furthermore, applying the same technique, we get explicit formulas for the determinant of a torus, a cylinder, and a M\"{o}bius ladder.
Cite
@article{arxiv.1212.4816,
title = {Determinants of grids, tori, cylinders and M\"{o}bius ladders},
author = {Khodakhast Bibak and Roberto Tauraso},
journal= {arXiv preprint arXiv:1212.4816},
year = {2012}
}