#16598: Useless new classes and a replacement for _check_pbd
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Reporter: ncohen | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.3
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Nathann Cohen | Work issues:
Report Upstream: N/A | Commit:
Branch: u/ncohen/16598 | cdaf1e2e834f3895d1fb096a139446bf8620d319
Dependencies: #16553 | Stopgaps:
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Changes (by vdelecroix):
* status: needs_review => needs_work
Comment:
Hey Nathann,
In group divisible design, there must be more parameters:
- `v` the size of the ground set
- `K` the admissible size of the blocks
- `G` the admissible size of the groups
The definition seems to be standard (see the big paper of Hanani and the
definition IV.1.3 of the Handbook)
Anyway, GDD is just a strict generalization of PBD and it is very clear
from Handbook IV.1.3.
That way, your `is_pbd` would just be a lambda function.
Actually, it would be nicer that `IncidenceStructure` would actually be a
`GroupDivisibleDesign` (groups being the partition into points). The
points can be ordered in such way that the groups are
{{{
0 1 ... g1-1|g1 g1+1 ... g1+g2-1|...
}}}
and then the new class would just need an extra `._group_sizes` attribute
that would be an integer partition.
Some methods are not well adapted to group divisible designs
- `dual`: is the dual well defined for GDD?
- `incidence_matrix`: must be the incidence matrix group/block (or put a
flag allowing to have points/blocks)
- `automorphis_group` is wrong since it must preserver the groups
Why do you use tuples where everywhere in `IncidenceStructure` there are
lists?
Would you mind having a "stupid" `.group_sizes()` method?
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16598#comment:4>
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