Derangements on the \(n\)-cube
type: Item
instance of: scholarly article
title: Derangements on the \(n\)-cube
zbMATH Open document ID: 0774.05002
DOI: 10.1016/0012-365X(93)90479-D
author: William Y. C. Chen
author: Richard P. Stanley
published in: Discrete Mathematics
publication date: 1993-06-20T00:00:00Z
review text: The \(2^ n\) vertices of the \(n\)-cube \(Q_ n\) are \(n\)-tuples of 0's and 1's. The vertices of a \(k\)-subcube \(G_ k\) have constant entries in \(n- k\) positions. A symmetry \(w\) of \(Q_ n\) fixes \(G_ k\) if the image of any vertex of \(G_ k\) is still a vertex of \(G_ k\). If \(w\) fixes no \(k\)-subcube then \(w\) is a \(k\)-derangement; otherwise \(w\) is a \(k\)- rearrangement. The authors establish a necessary and sufficient condition for a symmetry of \(Q_ n\) to have a fixed \(k\)-subcube. They also find a way to compute the generating function for the number of \(k\)- rearrangements on \(Q_ n\).
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05E99
zbMATH DE Number: 205591
zbMATH Keywords: \(n\)-cube
zbMATH Keywords: derangement
zbMATH Keywords: rearrangements
zbMATH Keywords: symmetry
zbMATH Keywords: generating function
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 205591