On the Distances between Latin Squares and the Smallest Defining Set Size | Zendy

Cavenagh Nicholas | Zendy; Ramadurai Reshma | Zendy

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On the Distances between Latin Squares and the Smallest Defining Set Size

Author(s) -

Cavenagh Nicholas,

Ramadurai Reshma

Publication year - 2017

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.21529

Subject(s) - latin square , mathematics , combinatorics , square (algebra) , set (abstract data type) , order (exchange) , discrete mathematics , statistics , geometry , computer science , chemistry , rumen , food science , finance , fermentation , economics , programming language

In this note, we show that for each Latin square L of order n ≥ 2 , there exists a Latin squareL ′ ≠ L of order n such that L and L ′ differ in at most 8 ncells. Equivalently, each Latin square of order n contains a Latin trade of size at most 8 n . We also show that the size of the smallest defining set in a Latin square is Ω ( n 3 / 2 ) .

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