On the combinatorics of derangements and related permutations
作者：
Highlights：
• Provide a bijection combinatorial proof for the facts that The number of derangements of length n equals the number of permutations of length n that have exactly one small ascent.
• Provide a bijection combinatorial proof for that The number of derangements of length n equals the number of non derangements of length n+1 with the largest and smallest fixed points differing by 2.
• Provide a bijection proof for that t he number of permutations of length n that have exactly one succession equals the number of permutations of length n that do not start with one and have no successions.
• Provide a simple bijection proof for that t he number of permutations of length n that do not start with 1 and have no consecutive right to left minima equals the number of desarrangements of length n.
摘要
•Provide a bijection combinatorial proof for the facts that The number of derangements of length n equals the number of permutations of length n that have exactly one small ascent.•Provide a bijection combinatorial proof for that The number of derangements of length n equals the number of non derangements of length n+1 with the largest and smallest fixed points differing by 2.•Provide a bijection proof for that t he number of permutations of length n that have exactly one succession equals the number of permutations of length n that do not start with one and have no successions.•Provide a simple bijection proof for that t he number of permutations of length n that do not start with 1 and have no consecutive right to left minima equals the number of desarrangements of length n.
论文关键词：Derangement,Permutation,Bijection
论文评审过程：Received 27 February 2022, Revised 14 June 2022, Accepted 16 June 2022, Available online 25 June 2022, Version of Record 25 June 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127341
