scholarly journals A Construction Method for Complete Sets of Mutually Orthogonal Frequency Squares

10.37236/1543 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
V C Mavron
Keyword(s):  
Construction Method ◽  
Complete Sets ◽  
Frequency Squares

A construction is described for combining affine designs with complete sets of mutually orthogonal frequency squares to produce other complete sets.

scholarly journals Frequency Squares and Affine Designs

10.37236/1534 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
V C Mavron
Keyword(s):  
Design Theory ◽  
Theory Construction ◽  
Basic Design ◽  
Complete Sets ◽  
Almost All ◽  
Two Parameter ◽  
Frequency Squares

The known methods for constructing complete sets of mutually orthogonal frequency squares all yield one of two parameter sets. We show that almost all these constructions can be derived from one basic design theory construction.

scholarly journals Mutually Orthogonal Binary Frequency Squares

10.37236/9373 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Thomas Britz ◽  
Nicholas J. Cavenagh ◽  
Adam Mammoliti ◽  
Ian M. Wanless
Keyword(s):  
Hadamard Matrix ◽  
Isomorphism Classes ◽  
Complete Set ◽  
Complete Sets ◽  
Frequency Squares ◽  
Ordered Pairs

A frequency square is a matrix in which each row and column is a permutation of the same multiset of symbols. We consider only binary frequency squares of order $n$ with $n/2$ zeros and $n/2$ ones in each row and column. Two such frequency squares are orthogonal if, when superimposed, each of the 4 possible ordered pairs of entries occurs equally often. In this context we say that a set of $k$-MOFS$(n)$ is a set of $k$ binary frequency squares of order $n$ in which each pair of squares is orthogonal. A set of $k$-MOFS$(n)$ must satisfy $k\le(n-1)^2$, and any set of MOFS achieving this bound is said to be complete. For any $n$ for which there exists a Hadamard matrix of order $n$ we show that there exists at least $2^{n^2/4-O(n\log n)}$ isomorphism classes of complete sets of MOFS$(n)$. For $2<n\equiv2\pmod4$ we show that there exists a set of $17$-MOFS$(n)$ but no complete set of MOFS$(n)$. A set of $k$-maxMOFS$(n)$ is a set of $k$-MOFS$(n)$ that is not contained in any set of $(k+1)$-MOFS$(n)$. By computer enumeration, we establish that there exists a set of $k$-maxMOFS$(6)$ if and only if $k\in\{1,17\}$ or $5\le k\le 15$. We show that up to isomorphism there is a unique $1$-maxMOFS$(n)$ if $n\equiv2\pmod4$, whereas no $1$-maxMOFS$(n)$ exists for $n\equiv0\pmod4$. We also prove that there exists a set of $5$-maxMOFS$(n)$ for each order $n\equiv 2\pmod{4}$ where $n\geq 6$.

Construction Method of Equivalent Systems for Bulk Power System

2009 ◽  
Vol 129 (5) ◽  
pp. 715-716
Author(s):  
Shoichi Minami ◽  
Satoshi Morii ◽  
Suo Lian ◽  
Shunji Kawamoto
Keyword(s):  
Power System ◽  
Construction Method ◽  
Equivalent Systems ◽  
Bulk Power
Sign in / Sign up

Export Citation Format

Share Document