An equidistribution involving invisible inversions

2021/11/04 by Coopman, Michael, Rubey, Martin
#05A05 #05A19 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.02973

Abstract

We provide two explicit bijections demonstrating that, among permutations, the number of invisible inversions is equidistributed with the number of occurrences of the vincular pattern 13-2 after sorting the set of runs.

Related

• A sextuple equidistribution arising in Pattern Avoidance
• A Simple Proof that Major Index and Inversions are Equidistributed
• Combinatorial Statistics on Pattern-avoiding Permutations
• Pattern Avoiding Permutations Enumerated by Inversions
• Burstein's permutation conjecture, Hong and Li's inversion sequence conjecture, and restricted Eulerian distributions