#18944: Posets: maximal_chains() partial-option broken
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       Reporter:  jmantysalo         |        Owner:
           Type:  defect             |       Status:  needs_info
       Priority:  major              |    Milestone:  sage-6.9
      Component:  combinatorics      |   Resolution:
       Keywords:  posets             |    Merged in:
        Authors:  Jori Mäntysalo     |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  u/jmantysalo/maximal_chains        |  e6a4ae2b1f7f887b58a49af5c1607640c7821dde
   Dependencies:                     |     Stopgaps:
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Comment (by jmantysalo):

 Replying to [comment:11 tscrim]:
 > I'm not opposed to changing the behavior to removing the saturated
 condition, but it would make the code a lot more complex (i.e., likely
 non-recursive).

 Not necessarily, as digraphs already have `all_paths(start, end)`. A PoC:

 {{{
 P = Posets.BooleanLattice(5)
 g = P.hasse_diagram()
 k = [1,11,31]
 for x in [flatten(c) for c in CartesianProduct(*[g.all_paths(k[i],k[i+1])
 for i in range(len(k)-1)])]:
     print [x[i] for i in range(len(x)) if x[i] != x[i-1]]
 }}}

 But in that case the name of the parameter should be `include`, not
 `partial`.

 I still think that we could remove it. Maybe with deprecation that
 mentions `_max_chains()`?

--
Ticket URL: <http://trac.sagemath.org/ticket/18944#comment:12>
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