sBruijn {Necklaces}

The de Bruijn sequence

Description

The function generates the (minimum) de Bruijn sequence of length n over an alphabet of m consecutive non-negative integers.

Usage

sBruijn(n=1,m=2, fn=0, bSep=FALSE)

Arguments

n

positive integer: the length of the representatives

m

positive integer: the number of consecutive non-negative integers in the alphabet

fn

integer: the first value of the alphabet, the default is 0

bSep

boolean: if TRUE, a separator is inserted between the output blocks

Details

The function generates the (minimum) de Bruijn sequence of order n over an alphabet of m consecutive non-negative integers. The parameter (fn) assigns the first value of the alphabet, which by default is equal to 0. If (bSep) is set equal to TRUE, a separator is inserted between the output blocks.

Value

string

the de Bruijn sequence

Note

The function calls the Necklaces function and the cNecklaces function in the Necklaces package.

Author(s)

Elvira Di Nardo [e-mail],
Giuseppe Guarino [e-mail]

References

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

Necklaces, cNecklaces, LyndonW, sBruijn

Examples

# Generate the de Bruijn sequence of length 4 on the binary alphabet
# {0,1}
sBruijn(4) 
# or equivalently 
sBruijn(4,2) 

# Generate the de Bruijn sequence of length 2 over the alphabet {0,1,2} 
sBruijn(2,3)

# Generate the de Bruijn sequence of length 2 over the alphabet {1,2,3}
sBruijn(2,3,1)

# Generate the de Bruijn sequence of length 2 over the alphabet {1,2,3} 
# with a block separator. 
sBruijn(2,3,1,TRUE)