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arXiv · 0708.3628

Recursive Structure and Bandwidth of Hales-Numbered Hypercube

Xiaohan Wang·Xiaolin Wu
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Abstract

The Hales numbered $n$-dimensional hypercube and the corresponding adjacency matrix exhibit interesting recursive structures in $n$. These structures lead to a very simple proof of the well-known bandwidth formula for hypercube, whose proof was thought to be surprisingly difficult. A related problem called hypercube antibandwidth, for which Harper proposed an algorithm, is also reexamined in the light of the above recursive structures, and a close form solution is found.

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Xiaohan Wang, Xiaolin Wu. 2007-08-27. Recursive Structure and Bandwidth of Hales-Numbered Hypercube. https://arxiv.org/abs/0708.3628

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