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Mar
15
answered Optimal strategy in a match picking game
Mar
15
comment Sorting circles sizes with points in integers lattice
Also, it's not quite the same thing, but you may be interested in the rational parametrization of the unit circle and the consideration of those points as a group‌​.
Mar
15
comment Sorting circles sizes with points in integers lattice
"Then I find the smallest radius for boxes of width W+1 and reject from the sorted list all the findings greater than W+1 smallest." I'm not sure I understand what this part is saying.
Mar
15
comment Settlers of Catan Boards possibilities
There are only 6 ways to rotate the board that put corners on corners. And I don't think it's obvious that you can just divide by the number or rotations to get the answer.
Mar
15
answered Settlers of Catan Boards possibilities
Mar
10
answered Why can a Nim sum be written as powers of 2?
Mar
8
revised What is the condition for the first root of a cubic function to be positive?
added important "real coefficients" assumption
Mar
8
comment What is the condition for the first root of a cubic function to be positive?
@Taladris In the cubic case, when you combine it with the discriminant, Descartes' Rule of Signs can be used to find the exact the number of positive roots. When the discriminant is positive so that there's only one real root, the real root is given by $x_1$, so the Rule of Signs can tell you if $x_1$ is positive in that case, but of course not in the three-real-root case.
Mar
8
answered What is the condition for the first root of a cubic function to be positive?
Mar
7
comment condition for a cubic to have a repeated root
You have to discard any non-real $x$ that satisfy that sextic, but otherwise this method will work, albeit not be too easy to handle.
Mar
7
answered condition for a cubic to have a repeated root
Mar
6
awarded  Yearling
Feb
28
comment Has this subset-sum game been studied?
While this is certainly a finite game of perfect information, etc. It doesn't split up (at least not obviously) as a disjoint sum of other games, which makes it less likely to appear in a resource on combinatorial games. I would suggest looking at/asking more general combinatorial sources.
Jan
17
comment If $x=\pi a y^{1/2}$ then why is $\frac{\partial^n}{\partial x^n}=-2\left(\frac{y^{3/2}}{\pi a}\right)^n \frac{\partial^n}{\partial y^n}$?
@Kurome Certainly you can use induction to get to an answer without using OEIS. It may be easiest to treat the odd $n$ cases and even $n$ cases in parallel since the number of terms you have goes up by one every time $n$ goes up by $2$.
Jan
17
answered If $x=\pi a y^{1/2}$ then why is $\frac{\partial^n}{\partial x^n}=-2\left(\frac{y^{3/2}}{\pi a}\right)^n \frac{\partial^n}{\partial y^n}$?
Jan
14
comment Why does the theory of the game Nim use binary digital sums?
@Ross Lessons in Play is a softer introduction, and Combinatorial Game Theory is more rigorous.
Jan
1
awarded  Revival
Oct
18
awarded  Revival
Oct
13
comment countable subset of surreal games
If you want to go beyond the surreals and use division, you're doomed because division doesn't generally make sense (and to the extent that it would inherit sense from game addition, it's not well defined: *+*=0, does that mean *=0/2?). I don't think you'll like this answer, but finite exact representations of surreals with infinite sign expansions can be written with standard fraction and ordinal notation. "1/3" is a finite exact representation of a surreal with an infinite sign expansion. "$1/\omega +\omega_1/\omega_2$ is a finite exact representation of an uncountably long sign expansion.
Oct
13
comment countable subset of surreal games
To address your last question first, division doesn't generally work out for non-surreal games, and to the extent that it does, it's not unique: Should * be considered 0/2 since *+*=0? You are likely doomed if you're looking to go beyond the surreals. -- The nice way to use division over some surreals with finite representations is to use the standard notation for rational numbers and ordinals, etc. $1/\omega+1/(1+1/\omega_1)$ is a finite string representing a surreal number that's not a rational. $1/3$ is a finite representationing a surreal number with infinite sign expansion. etc.