Package 'CombinS'

Title: Construction Methods of some Series of PBIB Designs
Description: Series of partially balanced incomplete block designs (PBIB) based on the combinatory method (S) introduced in (Imane Rezgui et al, 2014) <doi:10.3844/jmssp.2014.45.48>; and it gives their associated U-type design.
Authors: Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod
Maintainer: Mohamed Laib <[email protected]>
License: GPL-3
Version: 1.1-1
Built: 2025-01-30 04:36:36 UTC
Source: https://github.com/mlaib/combins

Help Index

The Combinatory Method (s) for the construction of rectangular PBIB designs

Description

The application of the Combinatory Method (s), with ss chosen in [2,l−1][2, l-1], on rectangular association scheme to obtain the configuration and the parameters of the PBIB design associated.

Usage

CombS(n, l, s)

Arguments

n

Number of lines of the association schemes array.
l

Number of columns of the association schemes array.
s

Number of the token treatments from the same row of the association scheme.

Details

  • For 2<s<l2 < s < l, we obtain a rectangular PBIB design.

  • For s=ls = l, we obtain a singular group divisible designs.

Value

A LIST :

  • PBIB The configuration of the PBIB.

  • Type The type of the design

  • V Number of treatments.

  • B Number of blocs.

  • R Repetition of each treatment.

  • K Size of blocs.

  • lamda Vector of m-lambda.

  • Resolvable Is the design Resolvable ?

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

Imane Rezgui, Z. Gheribi-Aoulmi (2014). New construction method of rectangular partially balanced incomplete block designs and singular group divisible designs, Journal of Mathematics and Statistics, 10, 45- 48.

M.N. Vartak 1955. On an application of Kronecker product of Matrices to Statistical designs. Ann. Math. Stat.,26(420-438).

See Also

UType

Examples

## Not run: 
n<-3
l<-3
s<-2
CombS(l,n,s)

## End(Not run)

Generalized rectangular right angular (4) design with λ4\lambda_4 = 0

Description

Gives the configuration and the parametres of the design obtained by the first construction method of GPBIB_4 (see 3.1.1 of the paper rezgui et al (2015)).

Usage

GPBIB4A(n, l, s, w)

Arguments

n

Number of lines of the association schemes array.
l

Number of columns of the association schemes array.
s

Number of the token treatments from the same row of the association scheme.
w

Number of the association scheme arrays.

Details

  • For s=ls = l, the previous method gives configuration of nested group divisible designs.

Value

A LIST :

  • PBIB The configuration of the PBIB.

  • Type The type of the design

  • V Number of treatments.

  • B Number of blocs.

  • R Repetition of each treatment.

  • K Size of blocs.

  • lamda Vector of m-lambda.

  • Resolvable Is the design Resolvable ?

Note

For w=2w=2, the GPBIB_4 is a rectangular right angular (4) (PBIB_4)

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

Imane Rezgui, Z. Gheribi-Aoulmi and H. Monod (2015). U-type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes, Applied mathematics, 6, 242-264.

Imane Rezgui, Z.Gheribi-Aoulmi and H. Monod, New association schemes with 4, 5 and 7 associated classes and their associated partially balanced incomplete block designs; Advances and Applications in Discrete Mathematics Vol.12 Issue 2 197-206.

See Also

GPBIB4B and UType

Examples

## Not run: 
n<-3
l<-3
s<-3
w<-3
GPBIB4A(n, l, s, w)

## End(Not run)

Generalized rectangular right angular (4) design with λ4\lambda_4 not equal to 0

Description

Gives the configuration and the parametres of the design obtained by the seconde construction method of GPBIB_4 (see 3.1.2 of the paper rezgui et al (2015)).

Usage

GPBIB4B(n, l, s, w)

Arguments

n

Number of lines of the association schemes array.
l

Number of columns of the association schemes array.
s

Number of the token treatments from the same row of the association scheme.
w

Number of the association scheme arrays.

Value

A LIST :

  • PBIB The configuration of the PBIB.

  • Type The type of the design

  • V Number of treatments.

  • B Number of blocs.

  • R Repetition of each treatment.

  • K Size of blocs.

  • lamda Vector of m-lambda.

  • Resolvable Is the design Resolvable ?

Note

For w=2w=2, the GPBIB_4 is a rectangular right angular (4) (PBIB_4)

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

Imane Rezgui, Z. Gheribi-Aoulmi and H. Monod (2015). U-type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes, Applied mathematics, 6, 242-264.

Imane Rezgui, Z.Gheribi-Aoulmi and H. Monod, New association schemes with 4, 5 and 7 associated classes and their associated partially balanced incomplete block designs; Advances and Applications in Discrete Mathematics Vol.12 Issue 2 197-206.

See Also

GPBIB4A and UType

Examples

## Not run: 
n<-3
l<-3
s<-3
w<-3
GPBIB4B(n, l, s, w)

## End(Not run)

Generalized rectangular right angular (5) design.

Description

gives the configuration and the parametres of the design obtained by the construction method of GPBIB_5 (see 3.2 of the paper rezgui et al (2015)).

Usage

GPBIB5(n, l, s, w)

Arguments

n

Number of lines of the association schemes array.
l

Number of columns of the association schemes array.
s

Number of the token treatments from the same row of the association scheme.
w

Number of the association scheme arrays.

Value

A LIST :

  • PBIB The configuration of the PBIB.

  • Type The type of the design

  • V Number of treatments.

  • B Number of blocs.

  • R Repetition of each treatment.

  • K Size of blocs.

  • lamda Vector of m-lambda.

  • Resolvable Is the design Resolvable ?

Note

For w=2w=2, the GPBIB_5 is a rectangular right angular (5) (PBIB_5).

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

Imane Rezgui, Z. Gheribi-Aoulmi and H. Monod (2015). U-type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes, Applied mathematics, 6, 242-264.

Imane Rezgui, Z.Gheribi-Aoulmi and H. Monod, New association schemes with 4, 5 and 7 associated classes and their associated partially balanced incomplete block designs; Advances and Applications in Discrete Mathematics Vol.12 Issue 2 197-206.

See Also

UType

Examples

## Not run: 
n<-3
l<-3
s<-3
w<-3
GPBIB5(n, l, s, w)

## End(Not run)

Generalized rectangular right angular (7) design with λi\lambda_{i} equal to λi+4\lambda_{i+4} (i=1,...,4)(i=1,...,4)

Description

gives the configuration and the parametres of the design obtained by the first construction method of GPBIB_7 (see 3.3.1 of the paper rezgui et al (2015))

Usage

GPBIB7A(n, l, s, w)

Arguments

n

Number of lines of the association schemes array.
l

Number of columns of the association schemes array.
s

Number of the token treatments from the same row of the association scheme.
w

Number of the association scheme arrays.

Value

A LIST :

  • PBIB The configuration of the PBIB.

  • Type The type of the design

  • V Number of treatments.

  • B Number of blocs.

  • R Repetition of each treatment.

  • K Size of blocs.

  • lambda Vector of m-lambda.

  • Resolvable Is the design Resolvable ?

Note

For w=2w=2, the GPBIB_7 is a rectangular right angular (7) (PBIB_7).

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

Imane Rezgui, Z. Gheribi-Aoulmi and H. Monod (2015). U-type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes, Applied mathematics, 6, 242-264.

Imane Rezgui, Z.Gheribi-Aoulmi and H. Monod, New association schemes with 4, 5 and 7 associated classes and their associated partially balanced incomplete block designs; Advances and Applications in Discrete Mathematics Vol.12 Issue 2 197-206.

See Also

GPBIB7B and UType

Examples

## Not run: 
n<-3
l<-3
s<-3
w<-3
GPBIB7A(n, l, s, w)

## End(Not run)

Generalized rectangular right angular (7) design with distinct λi\lambda_i (i=1,...,7)

Description

Gives the configuration and the parametres of the design obtained by the seconde construction method of GPBIB_7 (see 3.3.2 of the paper rezgui et al (2015)).

Usage

GPBIB7B(n, l, s, w)

Arguments

n

Number of lines of the association schemes array.
l

Number of columns of the association schemes array.
s

Number of the token treatments from the same row of the association scheme.
w

Number of the association scheme arrays.

Value

A LIST :

  • PBIB The configuration of the PBIB.

  • Type The type of the design

  • V Number of treatments.

  • B Number of blocs.

  • R Repetition of each treatment.

  • K Size of blocs.

  • lambda Vector of m-lambda.

  • Resolvable Is the design Resolvable ?

Note

For w=2w=2, the GPBIB_7 is a rectangular right angular (7) (PBIB_7).

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

Imane Rezgui, Z. Gheribi-Aoulmi and H. Monod (2015). U-type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes, Applied mathematics, 6, 242-264.

Imane Rezgui, Z.Gheribi-Aoulmi and H. Monod, New association schemes with 4, 5 and 7 associated classes and their associated partially balanced incomplete block designs; Advances and Applications in Discrete Mathematics Vol.12 Issue 2 197-206.

See Also

GPBIB7A and UType

Examples

## Not run: 
n<-3
l<-3
s<-3
w<-3
GPBIB7B(n, l, s, w)

## End(Not run)

U-type design via some PBIB designs

Description

Applies the Fang algorithm on our constructed designs to obtain the configuration and the parameters of the U-type design associated.

Usage

UType(lst)

Arguments

lst

The output of one of our package functions.

Value

A LIST :

  • v Number of runs.

  • r Number of factors.

  • UtypeDesign The configuration of the U-type design..

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

K.T. Fang, R.Li and A.Sudjanto (2006). Design ans Modeling for Computer Experiments. Taylor & Francis Group, LLC London.

Examples

## Not run: 
M<-GPBIB4A(4,4,2,2)
UType(M)

## End(Not run)