Log-Convexity and Fixed Points of Permutations

Key Points

• The aim is to prove the log-convexity of derangements and permutations with one fixed point.
• Utilized combinatorial proof techniques.
• Analyzed sequences of derangements for length n≥3.
• Applied modifications to extend the proof to permutations with one fixed point.
• Confirmed that derangements of length n form a log-convex sequence for n≥3.
• Established similar results for certain permutations of length n≥4 with one fixed point.
• Clarified limitations of generalizing log-convexity to permutations with k fixed points where k≥3.