2011/02/16 by Piera Manara, Manara, Piera, Claudio Perelli Cippo +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1102.3359
openalex publication_date 2011/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the fine structure of the sets of involutions avoiding either 4312 (I(4321)) or 3412 (I(3412)), connecting the point of view of the decomposition theorems with the one of the associated labelled Motzkin paths. The algebraic generating function of the simple involutions in I(4321) is given, together with other generating functions, while the set I(3412) is shown containing no simple involutions of length n>2. The reverse-complement bijection maintains the fine structures of I(4321) and trivially of I(3412).