kStatistics (version 2.0)

gpPart: General partition polynomial

Description

The function returns general partition polynomials.

Usage

gpPart(n = 0)

Arguments

n

integer

Value

string

expression of the general partition polynomial

Warning

The value of the first parameter is the same as the MFB function in the univariate with univariate case composition.

Details

Faa di Bruno's formula gives the coefficients of the exponential formal power series obtained from the composition f(g()) of exponential formal power series. General partition polynomials in the variables y1,...,yn are recovered from Faa di Bruno's formula obtained from the MFB function in the case "composition of univariate f with univariate g" by setting f[i]=ai and g[i]=yi, for each i from 1 to n.

References

C.A. Charalambides (2002) Enumerative Combinatoris, Chapman & Haii/CRC.

E. Di Nardo, G. Guarino, D. Senato (2011) A new algorithm for computing the multivariate Faa di Bruno's formula. Appl. Math. Comp. 217, 6286--6295. (download from http://arxiv.org/abs/1012.6008)

See Also

MFB

Examples

# NOT RUN {
# Return the general partition polynomial G[2], that is a2(y1^2) + a1(y2)
gpPart(2)

# Return the general partition polynomial G[5], that is a5(y1^5) + 10a4(y1^3)(y2) + 15a3(y1)(y2^2) 
# + 10a3(y1^2)(y3) + 10a2(y2)(y3) + 5a2(y1)(y4) + a1(y5)
gpPart(5)

# }