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On the Likelihood of Comparability in Bruhat Order

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arxiv math/0605490 v1 pith:7NZTPZEZ submitted 2006-05-17 math.PR math.CO

Adam Hammett , Boris Pittel This is my paper · ORCID
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keywords bruhatcomparablenumberorderpairspermutationsupperactual
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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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Cited by 2 Pith papers

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