Critical sets in Latin squares given that they are symmetric
نویسندگان
چکیده
منابع مشابه
Defining sets for Latin squares given that they are based on groups
We investigate defining sets for latin squares where we are given that the latin square is the Cayley table for some group. Our main result is that the proportion of entries in a smallest defining set approaches zero as the order of the group increases without bound.
متن کاملWeak critical sets in cyclic Latin squares
We identify a weak critical set in each cyclic latin square of order greater than 5. This provides the first example of an infinite family of weak critical sets. The proof uses several constructions for latin interchanges which are generalisations of those introduced by Donovan and Cooper.
متن کاملMinimal critical sets for some small Latin squares
A general algorithm for finding a minimal critical set for any latin square is presented. By implementing this algorithm, minimal critical sets for all the latin squares of order six have been found. In addition, this algorithm is used to prove that the size of the minimal critical set for a back circulant latin square of order seven is twelve, and for order nine is twenty. These results provid...
متن کاملLatin squares and critical sets of minimal size
IsotoIHsl:n that lower bounds for infinite N of order n. hand or computer, strong critical sets of minimum nOn-lS01110Tnitnc reduced latin squares of order less than or of order 6. These latin squares have been taken from 129 onwards. We summarise our results in Table the numbering system listed by Denes and Keedwell latin squares. This numbering system is based on the ,<:n,,-r1i',rrHl1<:rn cla...
متن کاملMore greedy defining sets in Latin squares
A Greedy Defining Set is a set of entries in a Latin Square with the property that when the square is systematically filled in with a greedy algorithm, the greedy algorithm succeeds. Let g(n) be the smallest defining set for any Latin Square of order n. We give theorems on the upper bounds of gn and a table listing upper bounds of gn for small values of n. For a circulant Latin square, we find ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Publikacije Elektrotehnickog fakulteta - serija: matematika
سال: 2007
ISSN: 0353-8893
DOI: 10.2298/petf0718038m