Changes between Initial Version and Version 13 of Ticket #19123


Ignore:
Timestamp:
09/02/15 11:12:13 (4 years ago)
Author:
jmantysalo
Comment:

Replying to 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")? :=))

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  • Ticket #19123

    • Property Cc ncohen tscrim added
    • Property Status changed from new to needs_work
    • Property Branch changed from to u/jmantysalo/vertically_decomposable
    • Property Commit changed from to ca909a0c05fee489a071ff672b9f3b5392ba8158
  • Ticket #19123 – Description

    initial v13  
    11This patch adds a function `is_vertically_decomposable` to finite lattices.
     2
     3For testing see https://oeis.org/A058800 ; for example
     4
     5{{{
     6sum([1 for L in Posets(6) if L.is_lattice() and
     7 not LatticePoset(L).is_vertically_decomposable()])
     8}}}
     9
     10returns 7 as it should.