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.