Bart Demoen and Phuong-Lan Nguyen, Minimal Embeddings of Latin Tableaux in Latin Squares, Volume 2018, Number 1, Pages 15-25, 2018

# Bart Demoen and Phuong-Lan Nguyen, Minimal Embeddings of Latin Tableaux in Latin Squares, Volume 2018, Number 1, Pages 15-25, 2018

Abstract: Minimal embeddings of Latin Tableaux $LT$ in strictly larger Latin Squares $LS$ are established. Embeddings of $LT(N)$ into $LS(N+2)$ are studied in particular: it is proven they exist if and only if $N+2$ is prime. For all other $N$, there exists a Latin Tableau $LT(N)$ with a minimal embedding in a larger Latin Squares $LS(N+k)$ for all $1 < k \leq N$. For odd $k > 3$ the proof depends on the validity of the Wide Partition Conjecture for Young Diagrams.

Keywords: Latin Tableau, Embedding, Latin Square.

Bart Demoen and Phuong-Lan Nguyen, Minimal Embeddings of Latin Tableaux in Latin Squares, International Journal of Advances in Mathematics, Volume 2018, Number 1, Pages 15-25, 2018