Enumerations relating braid and commutation classes

Abstract

We obtain an upper and lower bound for the number of reduced words for a permutation in terms of the number of braid classes and the number of commutation classes of the permutation. We classify the permutations that achieve each of these bounds, and enumerate both cases.

19 pages

References in corpus (2)

• Braid moves in commutation classes of the symmetric group
• Reduced decompositions and commutation classes

Cited by in corpus (5)

• Diameter of the commutation classes graph of a permutation
• Forced perimeter in Elnitksy polygons
• Interval and $\ell$-interval Rational Parking Functions
• Braid graphs in simply-laced triangle-free Coxeter systems are partial cubes
• Combinatorial foundations for geometric realizations of subword complexes of Coxeter groups