On the combinatorics of derangements and related permutations

Jie Zhang; Daniel Gray; Hua Wang; Xiao Dong Zhang

doi:10.1016/j.amc.2022.127341

On the combinatorics of derangements and related permutations

Jie Zhang, Daniel Gray, Hua Wang, Xiao Dong Zhang

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

A derangement is a permutation in which no entry is at its original position. The number of derangements of [n] is called the “derangement number” or “de Montmort number”, and is denoted by D_n. The sequence {D_n} enumerates, in addition to the number of derangements, many other permutations under various constraints. In this paper, we explore the connections between these combinatorial objects and provide bijective proofs. Some related enumerative problems are also mentioned.

Original language	English
Article number	127341
Journal	Applied Mathematics and Computation
Volume	431
DOIs	https://doi.org/10.1016/j.amc.2022.127341
State	Published - Oct 15 2022

Keywords

Bijection
Derangement
Permutation

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10.1016/j.amc.2022.127341

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AB - A derangement is a permutation in which no entry is at its original position. The number of derangements of [n] is called the “derangement number” or “de Montmort number”, and is denoted by Dn. The sequence {Dn} enumerates, in addition to the number of derangements, many other permutations under various constraints. In this paper, we explore the connections between these combinatorial objects and provide bijective proofs. Some related enumerative problems are also mentioned.

KW - Bijection

KW - Derangement

KW - Permutation

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JO - Applied Mathematics and Computation

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ER -

On the combinatorics of derangements and related permutations

Abstract

Keywords

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