#12150: upgrade defect() of a finite word
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Reporter: sstarosta | Owner: sstarosta
Type: enhancement | Status: needs_review
Priority: trivial | Milestone: sage-4.8
Component: combinatorics | Keywords: finite word, defect,
palindrome, pseudopalindrome
Work_issues: | Upstream: N/A
Reviewer: Vincent Delecroix | Author: Stepan Starosta
Merged: | Dependencies:
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Comment(by sstarosta):
Hi Sébastien,
thanks for the comment.
> On two letters a and b, am I right to say that abababab... and
babababab... are the only two words that are E-full where E is the
exchange of a and b?
Yes. To have finite defect implies some other properties, for instance,
there have to be overlaps at some point (in the infinite word).
> This is already done by the method lacunas (from which you can
regenerate the above list of repeated numbers). A lacuna is a position
where there are no new palindrome finishing there or equivalently, the
defect goes up by one. Here are some examples from the doctests :
>
> {{{
> sage: w = Word([0,1,1,2,3,4,5,1,13,3])
> sage: w.lacunas()
> [7, 9]
> sage: words.ThueMorseWord()[:100].lacunas()
> [8, 9, 24, 25, 32, 33, 34, 35, 36, 37, 38, 39, 96, 97, 98, 99]
> sage: f = WordMorphism({0:[1],1:[0]})
> sage: words.ThueMorseWord()[:50].lacunas(f)
> [0, 2, 4, 12, 16, 17, 18, 19, 48, 49]
> }}}
Ok, thanks! I forgot about that. I should maybe update the comment in that
method also and check if it works fine with the modifications done.
> Stepan, could you please post a another patch which would replace the
third and that would apply on the first two and that would contain only
modification made without merge?
My bad, I will do it as you suggest, I can replace the file so it should
be fine.
Thanks,
Stepan
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12150#comment:10>
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