A combinatorial proof of symmetry among minimal star factorizations

2011/09/21 by Tenner, Bridget Eileen · 1 citation
#05A05 #05A15 #05A19 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1109.4642

Abstract

The number of minimal transitive star factorizations of a permutation was shown by Irving and Rattan to depend only on the conjugacy class of the permutation, a surprising result given that the pivot plays a very particular role in such factorizations. Here, we explain this symmetry and provide a bijection between minimal transitive star factorizations of a permutation πhaving pivot k and those having pivot k'.

Cited by

• Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements

Related

• Star factorizations and noncrossing partitions
• Centrality of star and monotone factorisations
• Bijections and symmetries for the factorizations of the long cycle
• Transitive factorizations of permutations and geometry
• Transitive factorisations in the symmetric group, and combinatorial aspects of singularity theory