#15259: (v,4,1)-BIBD, Latin Squares and Orthogonal arrays
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Reporter: ncohen | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.13
Component: combinatorics | Keywords:
Merged in: | Authors: Nathann Cohen
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies: #15107
Stopgaps: |
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WUUUUHUUUUUUUUUUUUUUUUUU !!
This patch implements a construction from Douglas Stinson's book
"Combinatorial Designs: Constructions and Analysis" for (v,4,1)-BIBD, i.e.
decompositions of {{{K_v}}} into copies of {{{K_4}}}. It requires the
construction of some other combinatorial objects, like some Mutually
Orthogonal Latin Squares and Orthogonal Arrays, an so some theorems from
this book are akso implemented by this patch. Hoping that the new files
with get larger eventually `:-)`
I also fixed a bug in `AffineGeometryDesign` : a `List` is used instead of
a `Set`, and as a result blocks are returned several times. Example :
Before
{{{
sage: print designs.AffineGeometryDesign(2, 1, GF(2)).blocks()
[[0, 1], [0, 1], [0, 2], [0, 2], [0, 3], [0, 3], [1, 2],
[1, 2], [1, 3], [1, 3], [2, 3], [2, 3]]
}}}
After
{{{
sage: print designs.AffineGeometryDesign(2, 1, GF(2)).blocks()
[[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]]
}}}
Overall :
* A file named `bibd.py` now gathers `steiner_triple_systems` (moved there
from `block_designs.py`). It also implement the present construction, and
a general `BalancedIncompleteBlockDesign` is created to obtain both
steiner triple systems and `(v,4,1)`-BIBD.
* A file named `latin_squares.py` contains construction for mutually
orthogonal latin squares, as well as a function to compute the product of
two latin squares.
* A file named `orthogonal_arrays.py` contains constructions for
orthogonal arrays and transversal designs (which are a particular case of
orthogonal arrays.
The most important thing is that **even if all the code written there is
wrong** (and it is indeed very unclear at times), nothing is returned
without being checked first for correction.
Sooooooooooo well. It's rather safe `;-)`
Have fuuuuuuuuuuuuun !
Nathann
--
Ticket URL: <http://trac.sagemath.org/ticket/15259>
Sage <http://www.sagemath.org>
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