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Jul
26
comment Generate all De Bruijn sequences
@qwr, DFS as typically described in algorithms text visits each edge only once and each node only twice. I can see how tracing an Eulerian path could be thought of as both depth-first and a search, but to call it DFS is to invite confusion. And to generate all Eulerian cycles you need to backtrack.
Jul
18
comment Generate all De Bruijn sequences
en.wikipedia.org/wiki/De_Bruijn_sequence#Construction en.wikipedia.org/wiki/De_Bruijn_graph en.wikipedia.org/wiki/…
Jul
17
answered Generate all De Bruijn sequences
Jul
13
comment Game on simple finite graphs
I'm glad that I now know why our calculations disagreed.
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
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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