2008/12/02 by M. Barnabei, Marilena Barnabei, Barnabei, M. +6
Computer Science · Mathematics · #05A15 #05E15 #20B35 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications #Topological and Geometric Data Analysis #math.CO #msc:05A15 #msc:05E15 #msc:20B35
paper · pdf · doi:10.48550/arxiv.0812.0463
22 pages, 10 figures
openalex publication_date 2008/12/02 · arxiv created 2008/12/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show how a bijection due to Biane between involutions and labelled Motzkin paths yields bijections between Motzkin paths and two families of restricted involutions that are counted by Motzkin numbers, namely, involutions avoiding 4321 and 3412. As a consequence, we derive characterizations of Motzkin paths corresponding to involutions avoiding either 4321 or 3412 together with any pattern of length 3. Furthermore, we exploit the described bijection to study some notable subsets of the set of restricted involutions, namely, fixed point free and centrosymmetric restricted involutions.