[seqfan] Another hypercube sequence to think about

Brendan McKay Brendan.McKay at anu.edu.au
Fri Dec 9 02:15:39 CET 2022


In this paper <https://arxiv.org/abs/2212.03328> just appeared on the 
arXiv, the following sequence is defined.

Consider an n-cube in R^n.  How many hyperplanes are needed in order
to dissect all edges?

"Dissect" means that the hyperplane passes through the edge other than
at its endpoints.

It seems that n hyperplanes are needed if n is very small, but the paper
mentions that 5 hyperplanes suffice for n=6. Otherwise no actual numbers
are mentioned, but there might be more in the references.

Brendan.



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