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.

Covalence(D, S) : Inc, { IncPt } -> RngIntElt

Given a subset S of the point set of an incidence structure D, return the number of blocks of D that contain S.

IncidenceMatrix(D) : Inc -> ModMatRngElt

The incidence matrix of the incidence structure D.

pRank(D, p) : Inc, RngIntElt -> RngIntElt

The p-rank of the incidence structure D.