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.
A binary n by n matrix representing a collineation of
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
ith basic factor is present in the
jth effect of the
kth 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]
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)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.