- Introduction
- Construction of Incidence Structures and Designs
- The Point-Set and Block-Set of an Incidence Structure
- General Design Constructions
- The Construction of Related Structures
- Complement(D) : Inc -> Inc
- Dual(D) : Inc -> Inc
- Contraction(D, p) : Inc, IncPt -> Inc
- Contraction(D, b) : Inc, IncBlk -> Inc
- Residual(D, b) : Inc, IncBlk -> Inc
- Residual(D, p) : Inc, IncPt -> Inc
- Simplify(D) : Inc -> Inc
- Sum(Q) : [ Inc ] -> Inc
- Union(D, E) : Inc, Inc -> Inc
- Restriction(D, S) : IncNsp, { Incpt } -> IncNsp
- Example Design_related (H156E3)
- The Witt Designs
- Difference Sets and their Development
- Elementary Invariants of an Incidence Structure
- Elementary Invariants of a Design
- Operations on Points and Blocks
- p in B : IncPt, IncBlk -> BoolElt
- p notin B : IncPt, IncBlk -> BoolElt
- S subset B : { IncPt }, IncBlk -> BoolElt
- S notsubset B : { IncPt }, IncBlk -> BoolElt
- PointDegree(D, p) : Inc, IncPt -> RngIntElt
- BlockDegree(D, B) : Inc, IncBlk -> RngIntElt
- Set(B) : IncBlk -> { IncPt }
- Support(B) : IncBlk -> { Elt }
- IsBlock(D, S) : Inc, IncBlk -> BoolElt, IncBlk
- Line(D, p, q) : Inc, IncPt, IncPt -> IncBlk
- ConnectionNumber(D, p, B) : Inc, IncPt, IncBlk -> RngIntElt
- Example Design_pts-blks-ops (H156E7)
- Elementary Properties of Incidence Structures and Designs
- IsSimple(D) : Inc -> BoolElt
- IsTrivial(D) : Inc -> BoolElt
- IsSelfDual(D) : Inc -> BoolElt
- IsUniform(D) : Inc -> BoolElt, RngIntElt
- IsNearLinearSpace(D) : Inc -> BoolElt
- IsLinearSpace(D) : Inc -> BoolElt
- IsDesign(D, t: parameters) : Inc, RngIntElt -> BoolElt, RngIntElt
- IsBalanced(D, t: parameters) : Inc, RngIntElt -> BoolElt, RngIntElt
- IsComplete(D) : Inc -> BoolElt
- IsSymmetric(D) : Dsgn -> BoolElt
- IsSteiner(D, t) : Dsgn, RngIntElt -> BoolElt
- IsPointRegular(D) : IncNsp -> BoolElt, RngIntElt
- IsLineRegular(D) : IncNsp -> BoolElt, RngIntElt
- Resolutions, Parallelisms and Parallel Classes
- HasResolution(D) : Inc -> BoolElt, { SetEnum }, RngIntElt
- HasResolution(D, λ) : Inc, RngIntElt -> BoolElt, { SetEnum }
- AllResolutions(D) : Inc -> SeqEnum
- AllResolutions(D, λ) : Inc, RngIntElt -> SeqEnum
- IsResolution(D, P) : Inc, SetEnum[SetEnum] -> BoolElt, RngIntElt
- HasParallelism(D: parameters) : Inc, RngIntElt -> BoolElt, { SetEnum }
- AllParallelisms(D) : Inc -> SeqEnum
- IsParallelism(D, P) : Inc, SetEnum[SetEnum] -> BoolElt, RngIntElt
- HasParallelClass(D) : Inc -> BoolElt, { IncBlk }
- IsParallelClass(D, B, C) : Inc, IncBlk, IncBlk -> BoolElt, { IncBlk }
- AllParallelClasses(D) : Inc -> SeqEnum
- Example Design_resol-parallel (H156E8)
- Conversion Functions
- Identity and Isomorphism
- The Automorphism Group of an Incidence Structure
- Construction of Automorphism Groups
- AutomorphismGroup(D) : Inc -> GrpPerm, GSet, GSet, PowMap, Map
- AutomorphismSubgroup(D) : Inc -> GrpPerm, PowMap, Map
- AutomorphismGroupStabilizer(D, k) : Inc, RngIntElt -> GrpPerm, PowMap, Map
- PointGroup(D) : Inc -> GrpPerm, GSet
- BlockGroup(D) : Inc -> GrpPerm
- Aut(D) : Inc -> PowMapAut, Map
- Example Design_auto (H156E10)
- Action of Automorphisms
- Image(g, Y, y) : GrpPermElt, GSet, Elt -> Elt
- Orbit(G, Y, y) : GrpPerm, GSet, Elt -> GSet
- Orbits(G, Y) : GrpPerm, GSet -> [ GSet ]
- Stabilizer(G, Y, y) : GrpPerm, GSet, Elt -> GrpPerm
- Action(G, Y) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm
- ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm
- ActionKernel(G, Y) : GrpPerm, GSet -> GrpPerm
- IsPointTransitive(D) : Inc -> BoolElt
- IsBlockTransitive(D) : Inc -> BoolElt
- Example Design_automorphism (H156E11)
- Incidence Structures, Graphs and Codes
- Automorphisms of Matrices
- Bibliography
V2.28, 13 July 2023