Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/mainfunctions.R

This function relabels a balanced (t-1)-spread or a covering star *St(n, μ, t, t_0)* of `PG(n-1,2)`

according to the specified collineation matrix.

1 | ```
applyCollineation(C, spr)
``` |

`C` |
A binary n by n matrix representing a collineation of |

`spr` |
A balanced spread or star of |

This code applies the relabelling corresponding to a collineation matrix C to any given balanced spread or star of PG(n-1, 2). The spread should be formatted as a 3-dimensional array with `spr[i,j,k]`

indicating whether or not the `i`

th basic factor is present in the `j`

th effect of the `k`

th flat of `spr`

. The collineation is applied via a matrix multiplication modulo 2 (i.e., the calculations are done over GF(2)). See Spencer et al. (2019) for details.

A spread or star of the same dimensions as spr.

Neil Spencer, Pritam Ranjan, Franklin Mendivil

Spencer, N.A., Ranjan, P., and Mendivil, F., (2019), "Isomorphism Check for *2^n* Factorial Designs with Randomization Restrictions", Journal of Statistical Theory and Practice, 13(60),1-24 [https://doi.org/10.1007/s42519-019-0064-5]

`checkSpreadIsomorphism`

for checking the isomorphism of balanced spreads.

`checkStarIsomorphism`

for checking the isomorphism of balanced covering stars.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
## Example 1: relabelling a 1-spread of PG(3,2)
data(spreadn4t2a)
Collin <- cbind(c(1,0,0,1), c(0,0,1,1), c(1,1,1,1), c(0,1,1,1))
# Collin is the collineation matrix corresponding to
# A -> AD, B -> CD, C -> ABCD, D -> BCD
applyCollineation(Collin, spreadn4t2a)
## Example 2: Relabelling a star of PG(4,2) consisting of 4-flats.
data(starn5t3a)
Collin2 <- cbind(c(0,0,0,0,1), c(1,0,0,0,0), c(0,1,0,0,0), c(0,0,0,1,0), c(0,0,1,0,0))
# Collin2 is the collineation matrix corresponding to
# A -> E, B -> A, C -> B, D -> D, E -> C
applyCollineation(Collin2, starn5t3a)
``` |

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