A lower bound for the size of the largest critical sets in Latin squares

Details A lower bound for the size of the largest critical sets in Latin squares A lower bound for the size of the largest critical sets in Latin squares

2006-12-31

arxiv.org/abs/math/0701014v1

Bulletin of the Institute of Combinatorics and its Applications (Canada). 38 (2003) pp.19-22

Mathematics

Combinatorics

Scientific paper

A critical set in an $n \times n$ array is a set $C$ of given entries, such that there exists a unique extension of $C$ to an $n\times n$ Latin square and no proper subset of $C$ has this property. The cardinality of the largest critical set in any Latin square of order $n$ is denoted by $\lcs{n}$. We give a lower bound for $\lcs{n}$ by showing that $\lcs{n} \geq n^2(1-\frac{2 + \ln 2}{\ln n})+n(1+\frac {\ln (8 \pi)} {\ln n})-\frac{\ln 2}{\ln n}.$

Affiliated with

Also associated with

No associations

Rating

A lower bound for the size of the largest critical sets in Latin squares does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A lower bound for the size of the largest critical sets in Latin squares, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A lower bound for the size of the largest critical sets in Latin squares will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-294019