# Design Theory

A proposal for enhancing combinatorial configurations in sage. Original report propsal for MTU: masterspropsal.pdf (Be warned! there are things in that proposal that I think are pointless (like the logic syntax))

I would like to use this page to collect all the functionality that sage(actually, any CAS) is missing from the bowels of Design Theory that most researchers in the area have as old C code from the 90's.

Please also see the work describing the database of designs that has already been worked on at DesignTheory.org

## Desirable Classes/Attributes

Hypergraphs:

• Dual
• Simple
• Uniform
• rank
• anti-rank
• partial hypergraph generated by a set
• sub-hypergraphs
• maximum degree
• degree sequence for connected/uniform
• separable
• pendent vertices
• linear
• steiner system
• intersecting family
• max cardinality of an intersecting family
• star
• chromatic index
• coloured edge
• hereditary closure
• interval hypergraph
• coloured edge property
• conformal
• representative graph/line graph

Frames(the IRGDD kind of Frames):

• type
• sub-frames
• SOLS
• SOLSOM

GDDs:

• resolvable
• resolution classes
• partial resolution classes (Frames)
• multiple groups
• replication number
• sub-GDDs
• incomplete
• Weighting
• Functions finding blocks containing certain group profiles

Transversal Designs:

• incomplete transversal

PBDs:

Latin Squares:

• Idempotent
• Subsquares

MOLs:

• Spouce-Avoiding
• Bachelor Squares

Orthogonal Array:

Resolvable Designs:

Near Resolvable Designs:

Finite Planes:

• parallel lines

Symmetric Design:

• Regular

Packings and Coverings:

Difference Sets:

• Singer
• complements
• Shifts
• supplementary
• Multipliers
• Planar
• Chen
• Characters

Greedoids:

• rank
• closure
• minors
• extensions
• interval

Extremal graph theory:

Epsiolon Nets:

Affine Planes:

Projective Geometries:

• Ovals
• Desargues

Block Designs:

• Residual and Derived
• Bruck-Ryser-Chowla
• Triple Systems

Tournaments:

One Factorizations:

• Starters
• GA(2n)(general as well)
• GK(2n)

Room Squares:

• Starter
• Squbsquare
• Howell

Biblo (for the above list):

Beth, Jungnickel, Lenz - Design theory (v1;v2, 2nd ed)

Wallis - Introduction to combinatorial designs

Pach, Agarwal - Combinatorial Geometry