#19383: Up-down Posets, and Dimenson Poset
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Reporter: kdilks | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.10
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/kdilks/updowndimension19383 | 4248b4ce536dae263297152498707211867c85f1
Dependencies: | Stopgaps:
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Comment (by kdilks):
I don't think we should reject n=1,2 for the standard example. Just
because they're simple and can more easily be described in other ways
doesn't mean the definition doesn't make sense and should raise an error.
Sadly, "standard example" is the accepted terminology. I don't know what
the original source would be, but there are tons of papers that use the
term, and it's also mentioned on the Wikipedia page for Order-Dimension.
Suggestions for what to use?
For UpDownPoset, I just followed the convention that Wikipedia had
(although I think I reversed up steps and down steps...there's a reason I
didn't mark this for review yet). I don't see any real reason to exclude
"kind of incomplete" fences. It just makes the code more complicated, and
limits what kind of posets the user can create. Plus I'm not even sure
exactly how one would define an "incomplete" fence.
The more I think about it, the more I realize the code should be a little
more general to allow more cases. For example, we always start with an up
step...but what if we want a fence starting with a down step? What if
instead of wanting one down-step after every m up-steps, we want k down-
steps after every m up-steps?
I think what I really want is a method where you put in {{{n}}} and a
subset {{{D}}} of {{{[n-1]}}}, and it creates the poset on where
{{{i>i+1}}} if {{{i in D}}} and {{{i<i+1}}} otherwise. The motivation
being linear extensions of these posets are in bijection with permutations
that have descent set {{{D}}} (and the fence example corresponds to
alternating permutations). We could still have an UpDownPoset method that
does roughly what the code currently does to match what Wikipedia has as
the definition of those posets, but it would really just construct an
appropriate {{{D}}} based on the input and use the more general method.
Since all of poset examples isn't consistent with including {{{facade}}}
options, I'll make another ticket that focuses just on making
{{{poset_examples.py}}} consistent.
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New commits:
||[http://git.sagemath.org/sage.git/commit/?id=4248b4ce536dae263297152498707211867c85f1
4248b4c]||{{{eliminated extraneous lines and changed a doc string}}}||
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Ticket URL: <http://trac.sagemath.org/ticket/19383#comment:7>
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