Peter Taylor
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 Oct30 comment Math puzzle: 10 digit strings generations Not quite practical as a computational solution, but this can be reduced to the independent set problem on a graph of $10!$ nodes and $\frac{10! 7!}{2}$ edges. Oct15 comment Number of unlabeled simple graphs with $n$ nodes even for all $n\ge 5$? Ah, it doesn't have simple in the title so my search didn't find it. Thanks for adding the link. Oct15 comment Number of unlabeled simple graphs with $n$ nodes even for all $n\ge 5$? Are you referring to A005470 (in which case you seem to be missing the very important word planar from the question) or to a different sequence? Oct12 comment Counting all possible board positions in Quoridor @lameK, I got 55 by writing a short computer program, but as I used an obscure language to do it I didn't see any benefit to sharing it. I'll add some examples to the last paragraph. Oct6 comment Can anyone extend my findings for Langford Pairings? I don't actually see a question. If this is an attempt to follow David Eppstein's advice that for your ideas to be included in the Wikipedia page on Langford pairing you should first get them published, then you should be aware that he was talking about publication in a peer-reviewed journal, not on a Q&A site. Sep22 comment No simple closed form for Bell numbers The premise of your question is somewhat unclear, because "closed form" is a somewhat variable quantity. Unless you allow factorials in a closed form, I can't think of any basic combinatorial quantity which has one. Allowing them lets in binomial coefficients and therefore Catalan numbers, but what else? Such basic combinatorial quantities as Stirling numbers and the partition function don't have well-known closed forms. Aug19 comment The Day Camp Stacking Game Is rule 4 a repetition of rule 2 or is it trying to say something additional? (I assume that "clockwise" and "left" mean the same thing here). Aug6 comment Deformable circle from a cubic Bezier approximation What do you mean by "smoothness"? Do you want C2 continuity? G2? Something else? Jul31 comment Lower bound for a relative of the central binomial coeff @Raphael, can you explain why there's a singularity at $-2+\sqrt{5}$? I see singularities at $-2-\sqrt{5}$ and $\frac{1}{4}$. Jul30 comment Lower bound for a relative of the central binomial coeff @GerryMyerson, the central binomial coefficient has a rather neat product representation which allows an easy ad hoc proof of the bound. The only way I can see to get a similar product representation is to factor out a central binomial coefficient from each of the binomial coefficients in the second sum. Then bounding with $\frac{1}{\sqrt{m-2j-1}}\ge\frac{1}{\sqrt{m}}$ I get a non-Gosper-summable hypergeometric, and crudely bounding the terms to get a summable geometric sequence gives a worse bound than simply taking the first term of the original sum. Jul30 comment Prove equivalence of Diffie-Hellman shared secret @codeomnitrix, $a \equiv b\pmod c$ is a shorthand notation for $\exists k : a - b = ck$ Jul23 comment Transforming a latin square into a sudoku @EwanDelanoy, that was my first thought for a counterexample, but just permuting the rows to give leading column $147258369$ suffices. Jul23 comment Transforming a latin square into a sudoku And similarly for the 9x9 case it should suffice to fix the top-left 6x6 block. Jul18 comment What is the count of the strict partitions of n in k parts not exceeding m? The answer to "How many different sets $X_1, \ldots, X_m$...?" would seem to be $m$... Jul16 comment “I have found a dead body on my car.” This seems to be more a question about the English language than about mathematical logic. Jul13 comment common multiple polynominal time What is a common multiple of two real numbers? Or, as an alternative phrasing, why is $1$ not always a solution? Jul12 comment The number of partitions of $n$ and the $n$th Fibonacci number. The main difference would seem to be that the first is correct notation and the second is meaningless. When $\operatorname{mod}$ is used as an infix function from $\mathbb{Z}\times\mathbb{N}^+$ to $\mathbb{N}$ you shouldn't separate it from its first argument. $(P_n \operatorname{mod} F_n) = P_n$ looks like a bizarre way of writing $0 \le P_n < F_n$, but $P_n = P_n \pmod{F_n}$ just looks like a tautology with a typo of $=$ for $\equiv$. Jul12 comment Describing all points 4000 miles from the north pole It's impossible to answer the underlying question without first determining the model of the globe and the metric. I think that you're modelling the globe as a sphere (as opposed to an ellipsoid such as the WGS84) and measuring the 4000 miles in Euclidean 3-space (as opposed to geodesics on the surface of the globe). Is this correct? Jul9 comment Difficulty parsing combinatorics exercise I read this as counting pairs of partitions ($\lambda$ is a partition into distinct parts of $k$, $\mu$ is a partition into distinct parts of $l$) such that $k+l=m$, $\lambda$ has $n$ more parts than $\mu$ with the complication of the $0$s. Jul3 comment Finding double root of $x^5-x+\alpha$ And then we have $\gcd(x^5 - x + \alpha, 5x^4 - 1)$ $= \gcd(5x^4 - 1, 4x - 5\alpha)$ $= \gcd(4x - 5\alpha, \frac{3125}{256}\alpha^4 - 1)$, so in order for that GCD to be linear we require $\frac{3125}{256}\alpha^4 - 1 = 0$.