On the Likelihood of Comparability in Bruhat Order
Probability
2007-05-23 v1 Combinatorics
Abstract
The poset of permutations of [n] under Bruhat ordering is studied. We give nontrivial upper and lower bounds for the number of comparable pairs of permutations in both the weak and strong versions of this order. In light of numerical experiments, we conjecture that in either case the upper bound is qualitatively close to the actual number of comparable pairs.
Cite
@article{arxiv.math/0605490,
title = {On the Likelihood of Comparability in Bruhat Order},
author = {Adam Hammett and Boris Pittel},
journal= {arXiv preprint arXiv:math/0605490},
year = {2007}
}
Comments
28 pages, 8 figures