How Often Are Two Permutations Comparable?

Authors

Adam J. Hammett, Cedarville UniversityFollow
Boris Pittel, The Ohio State University

Document Type

Article

Publication Date

2008

Journal Title

Transactions of the American Mathematical Society

Volume

360

Issue

9

First Page

4541

Last Page

4568

Abstract

Two permutations of are comparable in the Bruhat order if one is closer, in a natural way, to the identity permutation, , than the other. We show that the number of comparable pairs is of order at most, and at least. For the related weak order, the corresponding bounds are and , where . In light of numerical experiments, we conjecture that for each order the upper bound is qualitatively close to the actual number of comparable pairs.

Keywords

Permutations, Bruhat order

Recommended Citation

Hammett, Adam J. and Pittel, Boris, "How Often Are Two Permutations Comparable?" (2008). Science and Mathematics Faculty Publications. 320.
https://digitalcommons.cedarville.edu/science_and_mathematics_publications/320