摘要：Given a permutation pattern say τ = τ1 ... τk ∈ Sk and permutation ω = ω1 ... ωn ∈ S , we say that ω contains the pattern τ if there exist 1 ≤ i1 < ... < ik ≤ n such that red(ωi1 ... ωik) = τ. Each subsequence in ω is known as an occurrence of the pattern ω. Conversely, if there exists no occurrence of τ in ω, then we say that the permutation ω avoids the pattern τ. The popularity of a pattern τ is the total number of copies of τ within all permutations of a set. In this work, we address popularity of length-3 patterns in Γ1 - non deranged permutations in two approaches; algebraically and algorithmically. We first establish algebraically that pattern τ1 is the most popular and pattern τ3, τ4 and τ5 are equipopular in GΓ1p. We further provide efficient algorithms that also report same results on popularity and equipopularity of patterns of length-3 in GΓ1p as obtained by the algebraic approach.
