multiplex (version 3.4)

wordT: The Word Table of Relations

Description

The Word Table of multiple relations.

Usage

wordT(x)

Value

An object of the `WordTable' class

gens

the generator relations

WT

the Word Table where "n" stands for `node' and "g" stands for `generator'

The generators do not have values in neither the `node' nor the `generator' of the Word table since they are not a product of any other element in the semigroup (cf. details for the rest of the values).

Arguments

x

an array; usually with three dimensions of stacked matrices where the multiple relations are placed.

Author

Antonio Rivero Ostoic

Details

The Word Table is a consequence of the Edge Table and the function gives a list of indexed elements in the complete semigroup.

In terms of the Cayley graph of the semigroup (cf. ccgraph, the collection of unique relations (both compound and generators) are represented by nodes. On the other hand, the generators are edges that record the result of post-multiplying the compound relations by the generators.

The labels for the elements can be retrieved by the strings function.

References

Cannon, J.J. ``Computing the ideal structure of finite semigroup,'' Numerische Mathematik, 18, 254-266. 1971.

Pattison, P.E. Algebraic Models for Social Networks. Cambridge University Press. 1993.

See Also

edgeT, semigroup, strings.

Examples

## Create the data: 2 binary relations among 3 elements
arr <- round( replace( array(runif(18), c(3,3,2)), array(runif(18),
       c(3,3,2))>.5, 1 ) )

## get the word table
wordT(arr)