Perfect Partitions
I was playing with a variant of my Containers of Water question where we were instead interested in solid weights on a scale. It occurred to me that, as is often the case, I should consider easier problems first and see what comes of them. Ultimately, this led me down a path towards the idea of a ‘perfect partition’ and a few papers published in the late 1800s by MacMahon. Here’s how that went:
Posted in Expository, Math.CO, Math.REC, Mathematics
Tagged combinatorics, MacMahon, math, mathematics, perfect partition, recreational mathematics, weights
2 Comments
maximize 
, where 
denotes the largest connected interval of results?
David Lowry-Duda October 17, 2019 at 3:17 pm on Notes from a talk at the Maine-Quebec Number Theory ConferenceThanks Peter! You're right --- and it's a nice reference. 
Peter Humphries October 7, 2019 at 4:03 am on Notes from a talk at the Maine-Quebec Number Theory ConferenceOmega results of this form using this method are presented quite nicely in Chapter 15 of Montgomery and Vaughan; they give applications towards sign changes of the Chebyshev psi function and of partial sums of the Mobius function. 
David Lowry-Duda June 16, 2019 at 1:55 am on Choosing functions and generating figures for “When are there continuous choices for the mean value abscissa?”At first, we chose 2 because it was the other "obvious" point that we hadn't yet specified. We already controlled the values at 0, 1, and 3. But I later realized it doesn't matter what point we choose. What we're really doing is adding one extra degree of freedom and using it to minimize the L2 norm of the derivative ---
PC June 16, 2019 at 1:14 am on Choosing functions and generating figures for “When are there continuous choices for the mean value abscissa?”Why did you choose 2 for the pt in the L2 part? What if you chose 1.5 or something? 
Donna ebert September 27, 2018 at 3:55 pm on AboutI appreciate your taking the time to reply. The version of FreeCell I play online does count taking a card from the tableau (and the Freecells) as a move when adding them to the foundation. I never realized others did not. 
Luis Alberto Torres Cruz September 23, 2018 at 9:50 am on An intuitive introduction to calculusGreat post! Thank you for taking the time to write this. Regarding the example on population growth, you state that if P'(t) = k*P(t), then P(t) = ae^(kt). But wouldn't a more general expression be: P(t) = ae^(kt+C1), where C1 is a constant?