[seqfan] Re: A212046 should have an analogue from Pippenger, "The hypercube of resistors, asymptotic expansions, and preferential arrangements"
israel at math.ubc.ca
israel at math.ubc.ca
Thu May 3 08:11:15 CEST 2012
This problem can be related to random walk on the lattice Z^2.
See http://www.math.dartmouth.edu/~doyle/docs/walks/walks.pdf
Robert Israel
Dept of Mathematics
University of British Columbia
On May 2 2012, Charles Greathouse wrote:
>I wonder if that constant should be added to the OEIS... if anyone has
>the EE chops to calculate it.
>
>Charles Greathouse
>Analyst/Programmer
>Case Western Reserve University
>
> On Wed, May 2, 2012 at 4:35 AM, Georgi Guninski <guninski at guninski.com>
> wrote:
>> 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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