Metrics on permutations with the same descent set

2024/05/10 by Alexander Diaz-Lopez, Diaz-Lopez, Alexander, Kathryn Haymaker +5 · 1 citation
Computer Science · Mathematics · #05A05 #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2405.06177

openalex publication_date 2024/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S_n be the symmetric group on the set [n]:=\1,2,…,n\. Given a permutation σ=σ₁σ₂ ⋯ σ_n ∈ S_n, we say it has a descent at index i if σ_i>σ_i+1. Let D(σ) be the set of all descents of σ and define D(S;n)=\σ∈ S_n | D(σ)=S\. We study the Hamming metric and ℓ_∞-metric on the sets D(S;n) for all possible nonempty S⊂[n-1] to determine the maximum possible value that these metrics can achieve when restricted to these subsets.

Cited by

• Metrics on Permutation Families Defined by a Restriction Graph

Related

• Metrics on permutations with the same peak set
• Metrics on Permutation Families Defined by a Restriction Graph
• Metrics on Signed Permutations with the Same Peak Set
• Asymptotic correlations of metrics on the symmetric groups
• A New Metric on Symmetric Group and Applications to Block Permutation Codes