[math-fun] Tropical summation formulae
I got this from Dan Piponi (@sigfpe on twitter): sum (a+b)^-2 (c+d)^-2 (a+b+c+d)^-2 = 1/24 where the sum is over all integers (a,b,c,d) with 1<=a<=b, 1<=c<=d Paper: Tropical formulae for summation over a part of SL(2, Z) Nikita Kalinin, Mikhail Shkolnikov https://arxiv.org/abs/1711.02089 -- Tom Duff. Branches broken off trees.
I read that in the Denver airport, but my sleep deprived brain couldn't process it. On Thu, Nov 9, 2017 at 9:22 AM, Tom Duff <td@pixar.com> wrote:
I got this from Dan Piponi (@sigfpe on twitter):
sum (a+b)^-2 (c+d)^-2 (a+b+c+d)^-2 = 1/24
where the sum is over all integers (a,b,c,d) with 1<=a<=b, 1<=c<=d
Paper: Tropical formulae for summation over a part of SL(2, Z) Nikita Kalinin, Mikhail Shkolnikov https://arxiv.org/abs/1711.02089
-- Tom Duff. Branches broken off trees.
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http://i.imgur.com/k6XfkGE.png On Thu, Nov 9, 2017 at 10:57 AM, Mark VandeWettering <mvandewettering@gmail.com> wrote:
I read that in the Denver airport, but my sleep deprived brain couldn't process it.
On Thu, Nov 9, 2017 at 9:22 AM, Tom Duff <td@pixar.com> wrote:
I got this from Dan Piponi (@sigfpe on twitter):
sum (a+b)^-2 (c+d)^-2 (a+b+c+d)^-2 = 1/24
where the sum is over all integers (a,b,c,d) with 1<=a<=b, 1<=c<=d
Paper: Tropical formulae for summation over a part of SL(2, Z) Nikita Kalinin, Mikhail Shkolnikov https://arxiv.org/abs/1711.02089
-- Tom Duff. Branches broken off trees.
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
As Warren Smith pointed out, there's an additional condition on this sum: ad-bc=1 On Thu, 9 Nov 2017, Tom Duff wrote:
I got this from Dan Piponi (@sigfpe on twitter):
sum (a+b)^-2 (c+d)^-2 (a+b+c+d)^-2 = 1/24
where the sum is over all integers (a,b,c,d) with 1<=a<=b, 1<=c<=d
Paper: Tropical formulae for summation over a part of SL(2, Z) Nikita Kalinin, Mikhail Shkolnikov https://arxiv.org/abs/1711.02089
-- Tom Duff. Eigenvectors.
participants (3)
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Mark VandeWettering -
Mike Stay -
Tom Duff