Random Linear Extensions of Grids
Combinatorics
2007-05-23 v1
Abstract
A grid poset -- or grid for short -- is a product of chains. We ask, what does a random linear extension of a grid look like? In particular, we show that the average "jump number," i.e., the number of times that two consecutive elements in a linear extension are incomparable in the poset, is close to its maximum possible value. The techniques employed rely on entropy arguments. We finish with several interesting questions about this wide-open area.
Cite
@article{arxiv.math/0602509,
title = {Random Linear Extensions of Grids},
author = {Joshua Cooper},
journal= {arXiv preprint arXiv:math/0602509},
year = {2007}
}
Comments
13 pages, no figures