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

dc.creatorHatami, Hamed
dc.creatorMahmoodian, Ebadollah S.
dc.date2006-12-31
dc.date.accessioned2026-07-07T07:37:56Z
dc.date.available2026-07-07T07:37:56Z
dc.descriptionA 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 $\lcs{n} \geq n^2(1-\frac{2 + \ln 2}{\ln n})+n(1+\frac {\ln (8 π)} {\ln n})-\frac{\ln 2}{\ln n}.$
dc.identifierhttps://arxiv.org/abs/math/0701014
dc.identifierhttp://arxiv.org/abs/math/0701014
dc.identifierBulletin of the Institute of Combinatorics and its Applications (Canada). 38 (2003) pp.19-22
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120950
dc.subjectCombinatorics
dc.subject05B15
dc.titleA lower bound for the size of the largest critical sets in Latin squares
dc.typetext

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