Interesting Esoterica

Hunting Rabbits on the Hypercube

Article by Jessalyn Bolkema and Corbin Groothuis
  • Published in 2017
  • Added on
We explore the Hunters and Rabbits game on the hypercube. In the process, we find the solution for all classes of graphs with an isoperimetric nesting property and find the exact hunter number of $Q^n$ to be $1+\sum\limits_{i=0}^{n-2} \binom{i}{\lfloor i/2 \rfloor}$. In addition, we extend results to the situation where we allow the rabbit to not move between shots.

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BibTeX entry

@article{HuntingRabbitsontheHypercube,
	title = {Hunting Rabbits on the Hypercube},
	author = {Jessalyn Bolkema and Corbin Groothuis},
	url = {http://arxiv.org/abs/1701.08726v1 http://arxiv.org/pdf/1701.08726v1},
	urldate = {2017-02-06},
	abstract = {We explore the Hunters and Rabbits game on the hypercube. In the process, we
find the solution for all classes of graphs with an isoperimetric nesting
property and find the exact hunter number of {\$}Q^n{\$} to be
{\$}1+\sum\limits{\_}{\{}i=0{\}}^{\{}n-2{\}} \binom{\{}i{\}}{\{}\lfloor i/2 \rfloor{\}}{\$}. In addition, we
extend results to the situation where we allow the rabbit to not move between
shots.},
	comment = {},
	archivePrefix = {arXiv},
	eprint = {1701.08726},
	primaryClass = {math.CO},
	collections = {Attention-grabbing titles,Easily explained,Protocols and strategies,Animals},
	year = 2017
}