#19123: LatticePoset: add is_vertically_decomposable
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Reporter: jmantysalo | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.9
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Jori Mäntysalo | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jmantysalo/vertically_decomposable|
ca909a0c05fee489a071ff672b9f3b5392ba8158
Dependencies: | Stopgaps:
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Changes (by jmantysalo):
* cc: tscrim (added)
Old description:
> This patch adds a function `is_vertically_decomposable` to finite
> lattices.
New description:
This patch adds a function `is_vertically_decomposable` to finite
lattices.
For testing see https://oeis.org/A058800 ; for example
{{{
sum([1 for L in Posets(6) if L.is_lattice() and
not LatticePoset(L).is_vertically_decomposable()])
}}}
returns 7 as it should.
--
Comment:
Replying to [comment:11 ncohen]:
> Could you also add to your docstring a reference toward a textbook that
defines this notion?
Duh. Counting Finite Lattices by Heitzig and Reinhold defines it "- -
contains an element which is neither the greatest not the least element of
L but comparable to every element of L." On the other hand, On the number
of distributive lattices by Erné and (same) Heitzig and Reinhold says "- -
if it is either a singleton or the vertical sum of two nonempty posets -
-", and vertical sum on two two-element lattice by their definition is the
two-element lattice.
I select tscrim as another random victim. Travis, should we define the
two-element lattice to be vertically decomposable or indecomposable?
(Or raise `OtherError("developers don't know how to define this")`? `:=)`)
--
Ticket URL: <http://trac.sagemath.org/ticket/19123#comment:13>
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