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On F -squares and their critical sets

Journal Article


Abstract


  • We define the notion of critical set of an F -square, following the definition of critical set in latin squares, and then give critical sets for certain classes of F -squares. We also generalise certain results obtained for critical sets of latin squares, and look at minimal such sets. We show that critical sets of F -squares need to be studied as well as critical sets for latin squares as the techniques used differ considerably. We obtain theorems for the sizes of critical sets of types F(n; 1, n-1), F(n; 1, 1, n-2), and F(n; 2,2,...,2).

Publication Date


  • 1999

Citation


  • Fitina, L. F., Seberry, J., & Sarvate, D. (1999). On F -squares and their critical sets. Australasian Journal of Combinatorics, 19, 209-230.

Scopus Eid


  • 2-s2.0-41549089780

Web Of Science Accession Number


Start Page


  • 209

End Page


  • 230

Volume


  • 19

Abstract


  • We define the notion of critical set of an F -square, following the definition of critical set in latin squares, and then give critical sets for certain classes of F -squares. We also generalise certain results obtained for critical sets of latin squares, and look at minimal such sets. We show that critical sets of F -squares need to be studied as well as critical sets for latin squares as the techniques used differ considerably. We obtain theorems for the sizes of critical sets of types F(n; 1, n-1), F(n; 1, 1, n-2), and F(n; 2,2,...,2).

Publication Date


  • 1999

Citation


  • Fitina, L. F., Seberry, J., & Sarvate, D. (1999). On F -squares and their critical sets. Australasian Journal of Combinatorics, 19, 209-230.

Scopus Eid


  • 2-s2.0-41549089780

Web Of Science Accession Number


Start Page


  • 209

End Page


  • 230

Volume


  • 19