Peter Taylor
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 Jul 13 comment Game on simple finite graphs @hardmath, "the smallest non-negative integer that is not already assigned to its neighbours". Since the only integers assigned to the neighbours are 2 and 2, the smallest unassigned non-negative one is 0. Jul 13 comment Game on simple finite graphs @hardmath, with both path(A,-1,K) and path(A,2,k) the value which will be played into the gap next to B can only be 0 or 1, and in particular is never -1 or 2 in either case; in fact, we could go further and say that for any $B \not\in \{0,1\}$, path(A,-1,K) = path(A,B,K). path(2,2,1) has only one possible move, which is to play 0 into the gap and lose, exactly as with path(-1,-1,1). Other discrepancies are (1,0,3), (1,0,5), (1,0,7), (2,0,7), (1,1,2), (1,1,7), (2,1,1), (2,1,5), (2,1,7). Jul 9 answered Game on simple finite graphs Jul 2 comment Game on simple finite graphs When working with paths, $a$ and $b$ are only going to be $0$ or $1$ for the most part: the exceptions are that filling the hole in $0?1$ requires a $2$ (although that's then a finished segment), and the $-1$ endpoint special case. One thing I don't understand from your table is that I think that $-1$ should be equivalent to $2$: in both cases, the node next to it will be either $0$ or $1$, with $1$ occurring only when the node at distance $2$ is $0$. Jun 30 comment Game on simple finite graphs Ah, hang on. That's not true for large values of $k$, because then a $0$ can be inserted in the middle of the path and the value of $b$ matters. I apologise for sending you down a blind alley. Jun 30 comment Game on simple finite graphs The $p(a,b,k)$ notation can be improved slightly by observing that the actual values of $a$ and $b$ don't matter: all that matters is $a - b$ and $b\mod 2$. Jun 21 answered Diagonal-free Sudoku grid Jun 21 reviewed Close Looking for Advice Self Study Analysis May 21 answered Triangular Array's Recursive Formula Breakdown Apr 27 comment Computing efficiently a small base to the power a large number Are you after exact results or results to some level of relative error? Apr 27 reviewed Close How do you formally construct the following proof regarding completeness and vector spaces? Apr 24 comment Is an empty parenthesis a valid mathematical expression? The meaning of mathematical notation is highly dependent on context. Which subfield(s) of mathematics are relevant to the case which interests you? And what is your motivation for the question: trying to interpret someone else's use of them, trying to justify using them yourself, trying to win a random bet, ...? Apr 23 awarded Steward Apr 23 reviewed Close Betti numbers over unital rings Apr 23 reviewed Close Finding position of point (in 3D space ) which are at x,y offset from corner of a rectangle in 3D world Apr 23 reviewed Close Select 100 integers from 1,2,…,200 Apr 22 reviewed Close Can't do NFA to DFA Apr 22 reviewed Close Drawing Bijections for one set Apr 22 reviewed Close What is the densest, most opaque way of saying two odd numbers add up to an even number? Apr 22 reviewed Leave Open Calculate the infinite sum $\sum_{1}^\infty \frac{\log{n}}{2n-1}$