Peter Taylor
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 Dec 21 comment A combinatorial game theory problem What do you mean by "vicinal squares"? Does that cover diagonally adjacent, orthogonally adjacent, or both? And why do you call this a combinatorial game theory problem? It seems to be a single combinatorial question. Dec 10 comment How to solve this tough recurrence relation? Cross-post on MO Nov 27 comment Give the generator polynomial of a binary cyclic [9, 2] code. FWIW I checked the factors of $x^9-1$ over $GF(2)$ and they're correct. Nov 25 comment Secret Santa Perfect Loop problem Why is $A\rightarrow B\rightarrow C\rightarrow D\rightarrow A$ the only perfect loop? What's wrong with e.g. $A\rightarrow C\rightarrow B\rightarrow D\rightarrow A$? Nov 15 comment Upper bound for the widest matrix with no two subsets of columns with the same vector sum Related Nov 15 comment Upper bound for the widest matrix with no two subsets of columns with the same vector sum It's not actually the case that "any column cannot be the linear combination of any 2 other columns" - if it were then the upper bound would be 1. The point is that general linear combination allows multiples other than 0 or 1, whereas property X does not. Nov 12 comment Counting all possible legal board states in Quoridor Sketch of an approach: augment the previous approach by a set of variables which track whether the cells above and below a row of intersections are reachable from the top row and from the bottom row, and another which tracks totals. This will increase the number of nodes in the graph by a factor of on the order of tens of thousands, but the number of edges won't increase by nearly such a big factor, so it should still be a feasible calculation. Nov 8 comment Counting all possible board positions in Quoridor @lameK, if you're happy with the answer then there's a tick-in-a-circle button which you can use to mark it as accepted. That takes it out of the "Unanswered questions" list, and will be appreciated by people looking for genuinely unanswered questions. As for tougher Quoridor questions, in principle I'm interested but I always have a few things on the go and I can't guarantee a quick response. If you want to discuss by e-mail then I have a catch-all for anything to cheddarmonk.org. Nov 4 comment Counting all possible board positions in Quoridor @lameK, that's right. There are 3344 ways to order one row. Oct 31 comment Polynomial factorisation - absolute value of coefficients Ah, that explains it. Oops. Oct 31 comment Polynomial factorisation - absolute value of coefficients You could also have $x^4+x^3-x^2-1 = (x-1)(x^3+2x^2+x+1)$. If I'm understanding arxiv.org/abs/0904.3057 correctly it claims that this is the unique quartic with height 1 and an irreducible factor of height greater than 1, in which case your example is a correction. Oct 30 comment Math puzzle: 10 digit strings generations Independent set problem Oct 30 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. Oct 15 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. Oct 15 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? Oct 12 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. Oct 6 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. Sep 22 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. Aug 19 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). Aug 6 comment Deformable circle from a cubic Bezier approximation What do you mean by "smoothness"? Do you want C2 continuity? G2? Something else?