Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Embedding orthogonal partial Latin squares


Author: Charles C. Lindner
Journal: Proc. Amer. Math. Soc. 59 (1976), 184-186
MSC: Primary 05B15
DOI: https://doi.org/10.1090/S0002-9939-1976-0409227-2
MathSciNet review: 0409227
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Two partial latin squares are orthogonal provided that when they are superimposed any ordered pairs obtained are distinct. The purpose of this paper is to show that any collection of pairwise orthogonal finite partial latin squares can be embedded into pairwise orthogonal finite latin squares.


References [Enhancements On Off] (What's this?)

  • [1] R. C. Bose and S. S. Shrikhande, On the falsity of Euler's conjecture about the nonexistence of two orthogonal Latin squares of order $ 4t + 2$, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 734-737. MR 21 #3343. MR 0104590 (21:3343)
  • [2] Trevor Evans, Embedding incomplete Latin squares, Amer. Math. Monthly 67 (1960), 958-961. MR 23 #A68. MR 0122728 (23:A68)
  • [3] B. Ganter, Endliche Vervollständigung endlicher partieller Steinerscher Systeme, Arch. Math., (Basel) 22 (1971), 328-332. MR 45 #3218. MR 0294145 (45:3218)
  • [4] -, Partial pairwise balanced designs (to appear).
  • [5] R. W. Quackenbush, Near vector spaces over $ GF(q)$ and $ (v,q + 1,1)$-BIBDs, Linear Algebra Appl. 10 (1975), 259-266. MR 0369099 (51:5335)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05B15

Retrieve articles in all journals with MSC: 05B15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0409227-2
Keywords: Partial latin square, orthogonal latin squares, block designs
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society