Talk:De Bruijn sequence

From Wikipedia, the free encyclopedia

to create a de-bruijn sequance, "find an Eularian cycle on a de-bruijn graph" is wrong, because Eularian cycle has to use every "edge" once, but to create a de-bruijn sequance need to use every "node" once on a de-bruijn graph.

the article is correct and you are wrong, 'to create a de-bruijn sequance need to use every "node" once on a de-bruijn graph' is incorrect.

I think that the article, which now says "by taking an Hamiltonian cycle of a complete graph of order kⁿ", is wrong. A Hamiltonian cycle over the complete graph is just an ordering of the kⁿ sequences, but since only some orderings give a de Bruijn sequence, this is meaningless. It should rather say "by taking a Hamiltonian cycle of an n-dimensional de Bruijn graph over k symbols. Am I wrong? --fudo 14:29, 10 July 2006 (UTC)

I was wondering the same thing. Since no-one else seems to have objected here over the past 2+ months, I'll be bold and commit it. —JLD 20:31, 28 September 2006 (UTC)

As I understand it, you do use every EDGE exactly once. Michael Hardy 22:26, 28 September 2006 (UTC)

... and now I've added a diagram and an accompanying explanation of why it's Eulerian and not Hamiltonian. Michael Hardy 23:43, 28 September 2006 (UTC)

Everything you said is correct, except for that "not". In fact, by following an Eulerian cycle over an n-dimensional de Bruijn graph, you obtain a de Bruijn sequence of order n + 1. Since it's easy to prove (by the definition) that the n + 1-dimensional de Bruijn graph is just the line graph of the n-dimensional one, an Eulerian cycle over the first corresponds exactly to a Hamiltonian cycle over the second one. Try it by yourself. I'll modify slightly the article, leaving your example (which is perfect) as is. --fudo 13:05, 4 October 2006 (UTC)

The early on sentence: "Taking A = {0,1}, there are two distinct B(2,3): 00010111 and 00011101, one being the reverse of the other." Those two sequences are not the reverse of each other. Either a) this should say there are 4 distinct, 00010111 and 00011101 and these two reversed, which appears correct to me or b.) the part about "one being the reverse of the other" should be taken out. 17:18, 5 November 2006 (UTC)

They are reverses of each other if you mod out by cyclic shifts. Michael Hardy 20:15, 6 November 2006 (UTC)

The initial example given (A={0,1}) does not contain the subsequence 110 (although its claimed "reverse" does). So what's going on?

Oh never mind -- it is cyclic, so the sequence is "properly" viewed including the wrap-around from back to front. So the initial B(2,3) contains 110 via the "final" ones + the "initial" zero.

[edit] Capitals

Why is "de Bruijn sequence" not written as "De Bruijn sequence", with capital D? At least in Dutch, the first character of a name has to be a capital, even if it is something like "de" or "van" (so meneer (mister) De Bruijn, but Nicolaas Govert de Bruijn) and I never learned that that's different in English. And after all, De Bruijn was a Dutchman.DaanAlberga 13:15, 8 June 2006 (UTC)

Then why is the initial d in lower case at [[1]]? Michael Hardy 23:52, 12 June 2006 (UTC)

The initial d only is in lower case when it is _not_ the first letter of his name. In "a de Bruijn sequence", the d _is_ the initial letter of his name. In your reference, the Dutch page about De Bruijn, one can see that as well. When it says "Nicolaas de Bruijn" or something like that, the d is in lower case, and when it just says "De Bruijn", the d is a capital. DaanAlberga 09:31, 13 June 2006 (UTC)