@deanrubinemath.bsky.social
Reposted
This formula is from Wildberger–Rubine's recent paper "A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode". Taking \\(c_0=c_1=c_2=1\\) we see that
\\[ x = \sum_{n\geq 0} C_n\\]
where \\(C_n = \frac{1}{1+n} \binom{2n}{n}\\) is the \\(n\\)th […]
[Original post on mathstodon.xyz]
\\[ x = \sum_{n\geq 0} C_n\\]
where \\(C_n = \frac{1}{1+n} \binom{2n}{n}\\) is the \\(n\\)th […]
[Original post on mathstodon.xyz]
May 7, 2025 at 4:18 AM
This formula is from Wildberger–Rubine's recent paper "A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode". Taking \\(c_0=c_1=c_2=1\\) we see that
\\[ x = \sum_{n\geq 0} C_n\\]
where \\(C_n = \frac{1}{1+n} \binom{2n}{n}\\) is the \\(n\\)th […]
[Original post on mathstodon.xyz]
\\[ x = \sum_{n\geq 0} C_n\\]
where \\(C_n = \frac{1}{1+n} \binom{2n}{n}\\) is the \\(n\\)th […]
[Original post on mathstodon.xyz]
Reposted
Thanks again. As mathematical research goes, this paper isn't overly difficult, so don't be scared of downloading the pdf folks. Much of the paper stems from doing our homework of problems 7.22 and 7.50 in Concrete Mathematics.
May 5, 2025 at 3:21 AM
Thanks again. As mathematical research goes, this paper isn't overly difficult, so don't be scared of downloading the pdf folks. Much of the paper stems from doing our homework of problems 7.22 and 7.50 in Concrete Mathematics.
Reposted
Coauthor here. G[n], a single natural number index, is a Catalan number, G[n]=C[n+1]. Similarly, G[0,0,0...,m_k] (with k-2 zeros) is a Fuss number, C[0,0,0,...,1+m_k]. If you mean for an arbitrary vector k, that's still unknown, though I have proven the conjecture about G[0,0,0,...,m_k,m_{k+1}].
May 3, 2025 at 4:00 PM
Coauthor here. G[n], a single natural number index, is a Catalan number, G[n]=C[n+1]. Similarly, G[0,0,0...,m_k] (with k-2 zeros) is a Fuss number, C[0,0,0,...,1+m_k]. If you mean for an arbitrary vector k, that's still unknown, though I have proven the conjecture about G[0,0,0,...,m_k,m_{k+1}].
Reposted
!!!
interestingengineering.com/science/math...
m.winfuture.de/news/150903
www.tandfonline.com/doi/epdf/10....
interestingengineering.com/science/math...
m.winfuture.de/news/150903
www.tandfonline.com/doi/epdf/10....
Math shaken: 200-year-old algebra rule falls to Geode number discovery
A mathematician has found a new way to solve complex polynomial equations without using radicals or infinity.
interestingengineering.com
May 14, 2025 at 10:45 AM
Reposted
Une formule mathématique dans un article du Monthly par N. J. Wildberger et D. Rubine.
www.tandfonline.com/doi/full/10....
www.tandfonline.com/doi/full/10....
May 15, 2025 at 6:50 AM
Une formule mathématique dans un article du Monthly par N. J. Wildberger et D. Rubine.
www.tandfonline.com/doi/full/10....
www.tandfonline.com/doi/full/10....
Reposted
This paper is getting hyped a lot as rewriting Galois on the topic of the impossibility of solving polynomials with degree >5 with radicals.
Of course, it doesn't do that at all, but it *is* very interesting and extraordinarily good on citing previous work. 🧵
www.tandfonline.com/doi/full/10....
Of course, it doesn't do that at all, but it *is* very interesting and extraordinarily good on citing previous work. 🧵
www.tandfonline.com/doi/full/10....
A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode
The Catalan numbers Cm count the number of subdivisions of a polygon into m triangles, and it is well known that their generating series is a solution to a particular quadratic equation. Analogousl...
www.tandfonline.com
May 2, 2025 at 9:42 PM
This paper is getting hyped a lot as rewriting Galois on the topic of the impossibility of solving polynomials with degree >5 with radicals.
Of course, it doesn't do that at all, but it *is* very interesting and extraordinarily good on citing previous work. 🧵
www.tandfonline.com/doi/full/10....
Of course, it doesn't do that at all, but it *is* very interesting and extraordinarily good on citing previous work. 🧵
www.tandfonline.com/doi/full/10....