On the Likelihood of Comparability in Bruhat Order

Details On the Likelihood of Comparability in Bruhat Order On the Likelihood of Comparability in Bruhat Order

2006-05-17

arxiv.org/abs/math/0605490v1

Mathematics

Probability

28 pages, 8 figures

Scientific paper

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.

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