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Completing partial latin squares with one nonempty row, column, and symbol
Other   Peer reviewed

Completing partial latin squares with one nonempty row, column, and symbol

Jaromy Kuhl and Michael W Schroeder
The Electronic Journal of Combinatorics, Vol.23(2), P2.23
Marshall Digital Scholar
DOI: https://doi.org/10.37236/5675

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Abstract

Let r,c,s ∈{1,2,…,n} and let PP be a partial latin square of order n in which each nonempty cell lies in row r, column c, or contains symbol s. We show that if n ∉ {3, 4, 5} and row r, column c, and symbol s can be completed in P, then a completion of P exists. As a consequence, this proves a conjecture made by Casselgren and Häggkvist. Furthermore, we show exactly when row r, column c, and symbol s can be completed.

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