Quasirandom Latin squares

We prove a conjecture by Garbe et al. [arXiv:2010.07854] by showing that a Latin square is quasirandom if and only if the density of every 2x3 pattern is 1/720+o(1). This result is the best possible in the sense that 2x3 cannot be replaced with 2x2 or 1xN for any N.

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Veröffentlicht in:	arXiv.org 2021-08
Hauptverfasser:	Cooper, Jacob W, Kral, Daniel, Ander Lamaison, Mohr, Samuel
Format:	Artikel
Sprache:	eng
Schlagworte:	Arrays
Online-Zugang:	Volltext
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Zusammenfassung:	We prove a conjecture by Garbe et al. [arXiv:2010.07854] by showing that a Latin square is quasirandom if and only if the density of every 2x3 pattern is 1/720+o(1). This result is the best possible in the sense that 2x3 cannot be replaced with 2x2 or 1xN for any N.
ISSN:	2331-8422