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# Talk:Complete paths

The article's title as it stands now is a charming throwback to the earliest day of wikis. But nowadays shouldn't it be Complete paths instead? Alonso del Arte 18:01, 26 April 2011 (UTC)

## Definition of non-extendable path

You wrote

We define a complete path as a non-extendable path within a bounded lattice.

I don't think "non-extendable path" is synonym with "longest path," or is it? — Daniel Forgues 00:35, 17 August 2011 (UTC)

A "non-extendable path" is not synonymous with "longest path". The length of a "non-extendable path" lies between two bounds.

The upper bound is the length of the "longest path" for a particular scenario.

The lower bound is:

• 3 for a non-self-adjacent path in a bounded square lattice
• 5 for a non-self-adjacent path in a bounded cubic lattice
• 4 for a non-self-intersecting path in a bounded square lattice
• 6 for a non-self-intersecting path in a bounded cubic lattice

Chris Gribble 21:59, 15 September 2011 (UTC)

Does it generalize to (for ${\displaystyle \scriptstyle d\,\geq \,1\,}$?)

• ${\displaystyle \scriptstyle 2d-1\,}$ for a non-self-adjacent path in a bounded ${\displaystyle \scriptstyle d\,}$-dimensional hypercubic lattice
• ${\displaystyle \scriptstyle 2d\,}$ for a non-self-intersecting path in a bounded ${\displaystyle \scriptstyle d\,}$-dimensional hypercubic lattice

Daniel Forgues 23:14, 17 September 2011 (UTC)

This seems like a reasonable conjecture.

Chris Gribble 18:07, 18 September 2011 (UTC)

I guess the 1-dimensional case is too trivial to be of interest, is it? — Daniel Forgues 19:28, 18 September 2011 (UTC)

I have already done an analysis of the 1D case and will include it for completeness.

Chris Gribble 21:54, 18 September 2011 (UTC)

A tentative treatment of the 1D case is now in the analysis section.

Chris Gribble 22:38, 18 September 2011 (UTC)

## In OEIS Wiki, a {{Stub}} is a short article in need of expansion.

I had added the {{Stub}} template because I thought that more could be added about complete paths in general, whether or not they are non-self-adjacent or non-self-intersecting. — Daniel Forgues 15:05, 4 June 2018 (EDT)

Since you say that you are currently working on this topic, I'm hinting that in that case I should not have put the {{Stub}} template yet. So I won't mark as a stub any article where some contributor says currently working on this topic. — Daniel Forgues 15:24, 4 June 2018 (EDT)