2006/05/17 by Adam J. Hammett, Adam Hammett, Hammett, Adam +2
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #math.CO #math.PR
paper · pdf · doi:10.48550/arxiv.math/0605490
28 pages, 8 figures
arxiv created 2006/05/17 · openalex publication_date 2006/05/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.