Avoiding arrays of odd order by Latin squares
(English)Manuscript (preprint) (Other academic)
We prove that there exists a constant c such that for each pos- itive integer k every (2k+1)×(2k+1) array A on the symbols 1,...,2k+1 with at most c(2k + 1) symbols in every cell, and each symbol repeated at most c(2k+1) times in every row and column is avoidable; that is, there is a (2k+1)×(2k+1) Latin square S on the symbols 1,...,2k+1 such that for each cell (i, j) in S the symbol in (i, j) does not appear in the corresponding cell in A. This settles the last open case of a conjecture by Häggkvist.
Latin square, avoidability, avoidable array
Research subject Mathematics
IdentifiersURN: urn:nbn:se:umu:diva-36026OAI: oai:DiVA.org:umu-36026DiVA: diva2:351491