ym2: Constructs Youden-m square designs and provides the...

In PBIBD: Partially Balanced Incomplete Block Designs

Constructs Youden-m square designs and provides the parameters of the corresponding PBIB design

Description

By omitting the middle 2t rows (where t = 1, 2, \ldots) from any even-ordered Circulant matrix with order v \geq 6, and considering only those rows that lie either above or below the omitted 2t rows, the resulting arrangement gives a new type of Youden-m square.

The columns of these Youden-m squares constitute m-associate class PBIB designs, with the following parameters:

• v \geq 6 and even, b = v, r = k = \frac{v}{2} - t

• \lambda_1 = r - 2, \lambda_m = \lambda_1 + 1

• If m is even, then:

  • \lambda_{i+1} = \lambda_i - 2 for i = 1, 2, \ldots, \frac{m}{2}

  • \lambda_{i-1} = \lambda_i - 2 for i = m, m-1, \ldots, \frac{m}{2} + 1

• If m is odd, then:

  • \lambda_{i+1} = \lambda_i - 2 for i = 1, 2, \ldots, \frac{m+1}{2}

  • \lambda_{i-1} = \lambda_i - 2 for i = m, m-1, \ldots, \left(\frac{m+1}{2}\right) + 1

Usage

ym2(n, t)

Arguments

n	n is the order of the circulant matrix, which is also the number of treatments
t	t is the number of rows to omit from the middle of the circulant matrix (i.e., 2t rows will be omitted)

Value

The function returns the required Youden-m square design and the parameters of the PBIB design constituted by taking the incomplete columns of the Youden-m square as blocks.

Author(s)

Kush Sharma, Davinder Kumar Garg

Examples

ym2(8, 1)

PBIBD documentation built on June 8, 2025, 10:10 a.m.