boundary_names: Calculation of boundary elements for quandle and rack boundary matrix
Description
This functions calculates the row and column names for both the quandle and the rack boundary matrix.
Usage
boundary_names(degree, k, degenerate)
Arguments
degree
Length of elements to be calculated. A positive integer.
k
Order of underlying rack/birack. This will be passed on to up/down action, if necessary. A positive integer.
degenerate
If true, remove degenerate entries (and hence calculate the names for the quandle boundary matrix). TRUE/FALSE.
Value
A matrix with $degree$ columns.
Details
This calculates all possible permutations of elements in $Z_k$ of length $degree$. If degenerate is true, it loops through all of them, removing the degenerate ones (that is, those where $x_i=x_i+1$, for an element $x=(x_i)_0^degree)$).