Elementary Invariants of an Incidence Structure
All operations defined for incidence structures apply also to near–linear spaces, linear spaces, and designs.
- NumberOfPoints(D): Inc -> RngInt
- # P: IncPtSet -> RngIntElt
The cardinality \(v\) of the point set \(P\) of the incidence structure \(D\).
- Points(D): Inc -> { IncPt }
An indexed set \(E\) whose elements are the points of the incidence structure \(D\). Note that this creates a standard set and not the point-set of \(D\), in contrast to the function
PointSet.
- Support(D): Inc -> { Elt }
An indexed set \(E\) which is the underlying point set of the incidence structure \(D\) (i.e., the elements of the set have their “real” types; they are no longer from the category IncPt).
- PointDegrees(D): Inc -> [ RngIntElt ]
A sequence whose \(i\)-th term gives the number of blocks containing the \(i\)-th point of the design \(D\).
- NumberOfBlocks(D): Inc -> RngIntElt
- # B: IncBlkSet -> RngIntElt
The number of blocks \(b\) of the incidence structure \(D\) with block-set \(B\).
- Blocks(D): Inc -> { IncBlk}
An indexed set containing the blocks of the incidence structure \(D\). In contrast to the function
BlockSet, this function returns the collection of blocks of \(D\) in the form of a standard set.
- BlockDegrees(D): Inc -> [ RngIntElt ]
- BlockSizes(D): Inc -> [ RngIntElt ]
A sequence whose \(i\)-th term gives the number of points in the \(i\)-th block of the incidence structure \(D\).