Ryser's conjecture on transversals in latin squares

A latin square of order nn is an n×nn\times n array filled with nn symbols so that each row and column contains every symbol exactly once. A transversal is a set of nn entries containing exactly one entry from each row and each column, with all nn symbols represented. Ryser's conjecture. Every latin square of odd order has a transversal. This is a classical existence conjecture concerning transversals in latin squares; the supplied source gives no resolution status.

Sources & referencesView supporting material

Primary source

Anna A. Taranenko, “Transversals, near transversals, and diagonals in iterated groups and quasigroups”, arXiv:2006.03786 (2021).

Additional references

8 papers in this index state this conjecture (2009–2020). The statement above is taken from the most recent of them; the others are arXiv:1912.11230, arXiv:1801.02893, arXiv:1801.10306, arXiv:1709.03071, arXiv:1605.01982, arXiv:1104.2702, arXiv:0903.5142.

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