Repetition in reduced decompositions

2011/06/14 by Bridget Eileen Tenner, Tenner, Bridget Eileen · 2 citations
Computer Science · Engineering · Mathematics · #05A05 #05A19 #05E15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1106.2839

openalex publication_date 2011/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a permutation w, we show that the number of repeated letters in a reduced decomposition of w is always less than or equal to the number of 321- and 3412-patterns appearing in w. Moreover, we prove bijectively that the two quantities are equal if and only if w avoids the ten patterns 4321, 34512, 45123, 35412, 43512, 45132, 45213, 53412, 45312, and 45231.

Cited by

• Cyclomatic numbers and permutations
• Majority relations for Condorcet domains of tiling type

Related

• The range of repetition in reduced decompositions
• Reduced word manipulation: patterns and enumeration
• Asymptotic enumeration of permutations avoiding generalized patterns
• Permutations Containing and Avoiding 123 and 132 Patterns
• Patterns and Fractions