On Minimal Defining Sets in AG(d,3)

Designs 2002 ◽  
2003 ◽  
pp. 103-131
Author(s):  
Diane Donovan ◽  
Abdollah Khodkar ◽  
Anne Penfold Street
Keyword(s):  
Defining Sets

scholarly journals On defining sets for projective planes

2005 ◽  
Vol 303 (1-3) ◽  
pp. 17-31 ◽  
Author(s):  
Endre Boros ◽  
Tamás Sz‘`onyi ◽  
Krisztián Tichler
Keyword(s):  
Projective Planes ◽  
Defining Sets

On The Spectrum of Minimal Defining Sets of Full Designs

2012 ◽  
Vol 30 (1) ◽  
pp. 141-157 ◽  
Author(s):  
Fatih Demirkale ◽  
Emine Şule Yazıcı
Keyword(s):  
Defining Sets

Two remarks about Sudoku squares

2006 ◽  
Vol 90 (519) ◽  
pp. 425-430 ◽  
Author(s):  
A. D. Keedwell
Keyword(s):  
Current Problem ◽  
Latin Square ◽  
Latin Squares ◽  
Critical Set ◽  
Critical Sets ◽  
The Given ◽  
A Current ◽  
Defining Sets

Smallest defining setsA standard Sudoku square is a 9 × 9 latin square in which each of the nine 3 × 3 subsquares into which it can be separated contains each of the integers 1 to 9 exactly once.A current problem is to complete such a square when only some of the cells have been filled. These cells are often called ‘givens’. (Such problems are currently (2005) published daily in British newspapers.) In more mathematical terms, the given filled cells constitute a defining set or uniquely completable set for the square if they lead to a unique completion of the square. If, after deletion of any one of these givens, the square can no longer be completed uniquely, the givens form a critical set. The investigation of critical sets for ‘ordinary’ latin squares is a topic of current mathematical interest. (See [1] for more details.)

Defining sets in combinatorics: a survey

2003 ◽  
pp. 115-174 ◽  
Author(s):  
D.M. Donovan ◽  
E.S. Mahmoodian ◽  
C. Ramsay ◽  
A.P. Street
Keyword(s):  
Defining Sets

scholarly journals A characterization of uniquely vertex colorable graphs using minimal defining sets

1999 ◽  
Vol 199 (1-3) ◽  
pp. 233-236 ◽  
Author(s):  
H. Hajiabolhassan ◽  
M.L. Mehrabadi ◽  
R. Tusserkani ◽  
M. Zaker
Keyword(s):  
Defining Sets

scholarly journals Some results on defining sets of t-designs

1999 ◽  
Vol 59 (2) ◽  
pp. 203-215 ◽  
Author(s):  
Brenton D. Gray ◽  
Colin Ramsay
Keyword(s):  
Infinite Family ◽  
Latin Squares ◽  
Critical Sets ◽  
Defining Sets

We investigate how varying the parameters of t-(ν, κ, λ) designs affects the sizes of smallest defining sets. In particular, we consider the effect of varying each of the parameters t, ν and λ. We establish a number of new bounds for the sizes of smallest defining sets and find the size of smallest defining sets for an infinite family of designs. We also show how one of our results can be applied to the problem of finding critical sets of Latin squares.

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