cBracelets {Necklaces} | R Documentation |
Elements in a bracelet
Description
The function generates the elements of a bracelet in equivalence relation with the vector given in input.
Usage
cBracelets(v=c(), bOut=FALSE)
Arguments
v |
vector: input vector |
bOut |
boolean: if |
Details
The function generates the elements of a bracelet which are in equivalence relation with the vector given in input. The first parameter is the input vector. If the second parameter (bOut
) is set equal to TRUE
,
the function produces a compact result.
Example: cBracelets(c(1,0,2,1))
produces the following result:
[1] 0 1 1 2 |
[1] 0 2 1 1 |
[1] 1 0 2 1 |
[1] 1 1 0 2 |
[1] 1 1 2 0 |
[1] 1 2 0 1 |
[1] 2 0 1 1 |
[1] 2 1 1 0 |
cBracelets(c(1,0,2,1),TRUE)
produces the following result:
[ 0 1 1 2 ] ( 1 ) |
[ 0 2 1 1 ] ( 2 ) |
[ 1 0 2 1 ] ( 3 ) |
[ 1 1 0 2 ] ( 4 ) |
[ 1 1 2 0 ] ( 5 ) |
[ 1 2 0 1 ] ( 6 ) |
[ 2 0 1 1 ] ( 7 ) |
[ 2 1 1 0 ] ( 8 ) |
Note that 0 1 1 2
is the representative of the class, that is the minimum in lexicographical order.
Value
list |
the list containing all the elements of the bracelet in equivalence relation with the vector given in input |
Note
The function is called from the fBracelets
function in the Necklaces
package.
Author(s)
Elvira Di Nardo elvira.dinardo@unito.it,
Giuseppe Guarino giuseppe.guarino@rete.basilicata.it
References
Di Nardo, E., and Guarino., G. (2022) kStatistics: Unbiased Estimates of Joint Cumulant Products from the Multivariate Faa Di Bruno's Formula. The R journal - In press. (https://arxiv.org/abs/2206.15348)
Di Nardo, E., and Guarino., G. (2022) Necklaces and bracelets in R - (https://arxiv.org/abs/2208.06855)
Flajolet, P., and Sedgewick, R. (2009) Analytic combinatorics. Cambridge University press.
See Also
Examples
# Generate the elements of the bracelet in equivalence relation with
# the input vector (1,0,2,1)
cBracelets(c(1,0,2,1))
# The previous result in a compact form
cBracelets(c(1,0,2,1),TRUE)