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# Publications

## Department of Mathematics & Statistics

### Publications

Representative Publications

(a) Books

- C. Laywine and G.L. Mullen,

*Discrete Mathematics Using Latin Squares*,

J. Wiley and Sons, New York (1998) 303 pages.

(b) Papers accepted in refereed research journals

- C. Laywine,

A derivation of an affine plane of order 4 from a triangle-free 3-colored K16,

*Discrete Math*,

to appear. - C. Laywine and G. Mullen,

A table of lower bounds for the number of mutually orthogonal frequency squares,

*Ars Combinatoria*,

to appear. - C. Laywine,

An affine design with*u = m2h*and*k = m2h-1*not equivalent to a complete set of*F(mh;mh-1)*,

MOFS,*Journal of Combinatorial Designs*7 (1999), pp. 331-340. - C. Laywine,

On the dimension of affine resolvable designs and hypercubes,

*Journal of Combinatorial Designs*4 (1996), pp. 235-246. - C. Laywine,

Frequency Squares,*CRC Handbook of Combinatorial Designs*,

C.J. Colbourn and J.H. Dinitz, Editors, CRC Press, Boca Raton, FL, (1996), pp. 354-357. - C. Laywine, G. Mullen and G. Whittle,

d-dimensional hypercubes and the Euler and MacNeish conjectures,

*Monatshefte fur Mathematik*119 (1995), pp. 223-238. - C. Laywine,

Complete sets of orthogonal frequency squares and affine resolvable designs,

*Utilitas Mathematica*43 (1993), pp. 161-170. - C. Laywine,

A counter-example to a conjecture relating complete sets of frequency squares and affine planes,

*Discrete Math.*122 (1993), pp. 255-262. - C. Laywine and G.L. Mullen,

Mutually orthogonal frequency hypercubes and affine geometries,

*Coding Theory, Design Theory, Group Theory: Proceedings of the Marshall Hall Conference*,

John Wiley & Sons. Inc. (1993), pp. 183-194. - C. Laywine,

Subsquares in orthogonal latin squares as subspaces in affine geometries:

A generalization of an equivalence of Bose,

*Designs, Codes, and Cryptography*, 3 (1992), pp. 21-28. - C. Laywine and G. Mullen,

Generalizations of Bose's equivalence between complete sets of mutually orthogonal latin squares and affine planes,

*Journal of Combinatorial Theory, Series A*, 61 (1992), pp. 13-35. - C. Laywine,

Complete sets of frequency squares with subsquares,

*Utilitas Mathematica*40 (1991), pp. 87-96. - C. Laywine, G. Mullen and S. Suchower,

Orthogonal frequency squares of type F(4t;t),

*Utilitas Mathematica*37 (1990), pp. 207-214. - C. Laywine and G. Mullen,

Mutually orthogonal frequency squares with non-constant frequency vectors,

*Ars Combinatoria*29 (1990), pp. 259-264.

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