Theory of limits of sequences of Latin squares

GARBE, Frederik, Robert Arthur HANCOCK, Jan HLADKY and Maryam SHARIFZADEH PHD. Theory of limits of sequences of Latin squares. Acta Mathematica Universitatis Comenianae. Bratislava: Comenius University, 2019, vol. 88, No 3, p. 709-716. ISSN 0231-6986.

Basic information

• Original name: Theory of limits of sequences of Latin squares
• Authors: GARBE, Frederik, Robert Arthur HANCOCK (826 United Kingdom of Great Britain and Northern Ireland, belonging to the institution), Jan HLADKY and Maryam SHARIFZADEH PHD.
• Edition: Acta Mathematica Universitatis Comenianae, Bratislava, Comenius University, 2019, 0231-6986.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10201 Computer sciences, information science, bioinformatics
• Country of publisher: Slovakia
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• RIV identification code: RIV/00216224:14330/19:00113863
• Organization unit: Faculty of Informatics
• UT WoS: 000484349000055
• Keywords in English: limit theory; latin squares
• Tags: International impact, Reviewed

Abstract

We build up a limit theory for sequences of Latin squares, which parallels the theory of limits of dense graph sequences. Our limit objects, which we call Latinons, are certain two variable functions whose values are probability distributions on [0, 1]. Left-convergence is defined using densities of k x k subpatterns in finite Latin squares, which extends to Latinons. We also provide counterparts to the cut distance, and prove a counting lemma, and an inverse counting lemma.