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?
Vaskor Basak December 25, 2021 at 4:40 am on Prime rich and prime poorWhat polynomials are allowable for prime-poor polynomials? Could I claim that I have found a better example of a prime-poor polynomial than x^12+488669 by presenting the example (x+3)^12-488601, for example? https://davidlowryduda.com/prime-rich-and-prime-poor/ 
David Lowry-Duda October 19, 2021 at 7:14 pm on An Intuitive Overview of Taylor SeriesHi Bob! The behavior of $c$ is actually quite subtle. It's not true that $c$ is actually a constant. For "nice" functions, what is true is that the mean value $c$ varies continuously over intervals (except at finitely many points). Combined with a form of Darboux's theorem (stating that every function that is the derivative of another function has the ---
Bob October 18, 2021 at 6:09 pm on An Intuitive Overview of Taylor SeriesIt's been a while since there was a comment here, but I'll give it a try in the hope for a response. Your proof gives me a sense of validation in my own work, although I still have questions. I wrote a very similar idea here: https://math.stackexchange.com/q/4277898/225136 . As you can see from a comment that someone left, the proof ---
Yavor Kirov April 14, 2021 at 3:24 am on Long live opalstack!Thabk you! I was looking for an opinion of a long-term user of Opalstack so your answer was exactly what I needed. 
Tomek March 18, 2021 at 5:09 pm on A response to FtYoU’s question on RedditGod bless you David. Great explanation! 
Jan van Delden February 25, 2021 at 5:07 pm on phase_mag_plot: a sage package for plotting complex functionsI took the liberty to download your SageMath module and changed a few options. Since I was not completely clear on the interaction between lightness and color (defined by the argument of the function to be displayed) I decided to weigh these differently. Color, from the colorwheel by 0.8 and lightness by 0.2. I computed the color first and weighed ---
eliot December 23, 2020 at 4:07 pm on Trigonometric and related substitutions in integralsFor Euler substitutions, do you mind explaining the reasoning for the t term in x*sqrt(a) + t. Is there anywhere else I can read up on this? Thanks for this post!