Comments on: Playing with Partitions: Euler’s Pentagonal Theorem http://math.blogoverflow.com/2014/08/25/playing-with-partitions-eulers-pentagonal-theorem/ The Mathematics Stack Exchange Blog Fri, 18 Sep 2015 11:57:28 +0000 hourly 1 https://wordpress.org/?v=4.5.6 By: Mathlover http://math.blogoverflow.com/2014/08/25/playing-with-partitions-eulers-pentagonal-theorem/#comment-1637 Thu, 20 Nov 2014 15:48:30 +0000 http://math.blogoverflow.com/?p=238#comment-1637 Hi @Paramanand Singh Is there any way to use the same technics for squared partition function? Please see my question in Mathoverflow. http://mathoverflow.net/questions/187377/generating-function-of-distinct-way-of-partitioned-square-sums-of-positive-integ

Thanks

]]> By: hardmath http://math.blogoverflow.com/2014/08/25/playing-with-partitions-eulers-pentagonal-theorem/#comment-384 Thu, 25 Sep 2014 23:19:08 +0000 http://math.blogoverflow.com/?p=238#comment-384 There’s a downloadable podcast of a 15 minute segment to be broadcast on Oct. 1 available from the (currently second) link on this BBC News page, Hardy and Ramanujan.

]]> By: Paramanand Singh http://math.blogoverflow.com/2014/08/25/playing-with-partitions-eulers-pentagonal-theorem/#comment-363 Mon, 22 Sep 2014 17:26:51 +0000 http://math.blogoverflow.com/?p=238#comment-363 @Jyrki Lahtonen Yeah the presentation is available in Hardy’s and Wright’s famous “An Introduction to the Theory of Numbers”, but I had read from some other book (which I can’t recall now). My natural reaction after learning this technique was to write a program to compute partitions and as you say I also had to implement arbitrary precision integer arithmetic library.

BTW do you have the link to that BBC documentary? It will be helpful for me and the blog visitors.

]]> By: Jyrki Lahtonen http://math.blogoverflow.com/2014/08/25/playing-with-partitions-eulers-pentagonal-theorem/#comment-340 Fri, 19 Sep 2014 09:34:25 +0000 http://math.blogoverflow.com/?p=238#comment-340 You can find this piece of theory described in Hardy & Wright. I once saw a (BBC?) documentary on Ramanujan. Complete with the 1729-story. There they told that Hardy assigned an assistant (or a grad student) the task to calculate $latex p(200)$. As the documentary didn’t describe the theory of generating functions a fellow grad student was in shock thinking that the dude had to list those partitions. I had to show him that you only need a relatively simple snippet of code to do this. This was in the 16-bit era, so the most tasking part was to implement the necessary bits of large integer operations 🙂

]]> By: Paramanand Singh http://math.blogoverflow.com/2014/08/25/playing-with-partitions-eulers-pentagonal-theorem/#comment-313 Sat, 13 Sep 2014 02:04:40 +0000 http://math.blogoverflow.com/?p=238#comment-313 I normally use MS Word drawing toolbar for the line drawings. It is simple and convenient and is good enough for most drawings.

]]> By: Paramanand Singh http://math.blogoverflow.com/2014/08/25/playing-with-partitions-eulers-pentagonal-theorem/#comment-312 Sat, 13 Sep 2014 02:02:49 +0000 http://math.blogoverflow.com/?p=238#comment-312 This is something I learned long back (1999 or so) when I was in college. I made some notes on Franklin proof and this post is based on those handwritten notes.

I will try to find something on Ramanujan/Hardy for my next post.

]]> By: vzn http://math.blogoverflow.com/2014/08/25/playing-with-partitions-eulers-pentagonal-theorem/#comment-311 Fri, 12 Sep 2014 16:11:51 +0000 http://math.blogoverflow.com/?p=238#comment-311 nice analysis. where did you learn all that? do you have some favorite refs on the subj? there seem to be applications of partitions in physics maybe. would be interested to hear of applications. hardy, lover of pure mathematics without known or likely applications, might be a bit aghast to find that out. hardy/ ramanujan, one of the great(est) math collaborations of all time, it would be great to read more about it in this blog sometime. a few hardy quotes also in this recent blog Fields/Nevanlinna prize 2014

]]> By: anorton http://math.blogoverflow.com/2014/08/25/playing-with-partitions-eulers-pentagonal-theorem/#comment-304 Thu, 11 Sep 2014 15:22:02 +0000 http://math.blogoverflow.com/?p=238#comment-304 I realize this comment isn’t related to the topic of you post, but it is related to its content: how did you create the graphics to demonstrate the pairing of partitions? They are very nice…

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