DOAJ Open Access 2009

Enumeration of derangements with descents in prescribed positions

Niklas Eriksen Ragnar Freij Johan Wästlund

Lihat Sumber DOI

Abstrak

We enumerate derangements with descents in prescribed positions. A generating function was given by Guo-Niu Han and Guoce Xin in 2007. We give a combinatorial proof of this result, and derive several explicit formulas. To this end, we consider fixed point $\lambda$-coloured permutations, which are easily enumerated. Several formulae regarding these numbers are given, as well as a generalisation of Euler's difference tables. We also prove that except in a trivial special case, if a permutation $\pi$ is chosen uniformly among all permutations on $n$ elements, the events that $\pi$ has descents in a set $S$ of positions, and that $\pi$ is a derangement, are positively correlated.

Topik & Kata Kunci

Mathematics

Penulis (3)

Niklas Eriksen

Ragnar Freij

Johan Wästlund

Format Sitasi

APA MLA BibTeX

Eriksen, N., Freij, R., Wästlund, J. (2009). Enumeration of derangements with descents in prescribed positions. https://doi.org/10.46298/dmtcs.2738

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2738

Informasi Jurnal

Tahun Terbit: 2009
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2738
Akses: Open Access ✓