The Initial Involution Patterns of Permutations

For a permutation π = π1π2 · · · πn ∈ Sn and a positive integer i ≤ n, we can view π1π2 · · · πi as an element of Si by order-preserving relabeling. The j-set of π is the set of i’s such that π1π2 · · · πi is an involution in Si. We prove a characterization theorem for j-sets, give a generating function for the number of different j-sets of permutations in Sn. We also compute the numbers of permutations in Sn with a given j-set and prove some properties of them.

• Type: Journal
• Year: 2007
• Where: COMBINATORICS
• Authors: Dongsu Kim, Jang Soo Kim
• Keywords: COMBINATORICS 2007, Order-preserving Relabeling, Permutations, Positive Integer