[seqfan] Re: A212046 should have an analogue from Pippenger, "The hypercube of resistors, asymptotic expansions, and preferential arrangements"
Georgi Guninski
guninski at guninski.com
Wed May 2 10:35:08 CEST 2012
Speaking of resistors, kxcd has an interesting problem about
infinite grid of ideal one ohm resistors:
http://xkcd.com/356/
On Tue, May 01, 2012 at 11:25:55AM -0700, Jonathan Post wrote:
> Shouldn't there be a 4-D analogue of A212046 Denominators in the
> resistance triangle: T(k,n)=b, where b/c is the resistance distance
> R(k,n) for k resistors in an n-dimensional cube.
>
> See:
> Nicholas Pippenger, "The hypercube of resistors, asymptotic
> expansions, and preferential arrangements", arXiv: 0904.1757v1,
> [math.CO], Apr 10, 2009, and also cites a 1914 book by Brooks and
> Poyser.
>
> Right now my PC refuses to open arxiv.org, so I can't easily supply
> the fractions, nor formula given.
>
> I am referring at the moment to a preview on
> http://www.researchgate.net/publication/24269095_The_Hypercube_of_Resistors_Asymptotic_Expansions_and_Preferential_Arrangements
>
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