Issue: 2027/Vol.37/No.1, Pages 1
LATIN RECTANGLES AND STABLE MATCHINGS IN MANY-SIDED PROBLEMS
Marcin Anholcer
This is not yet the definitive version of the paper. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article.
Cite as: M. Anholcer. Latin rectangles and stable matchings in many-sided problems. Operations Research and Decisions 2027: 37(1). DOI 10.37190/ord/236718
Abstract
In 1962, Gale and Shapley proved that there exists a stable matching in every instance of the 2-Sided Stable Matching Problem. It was shown very quickly that it does not have to be true in the case of 3-Sided Stable Matching Problems (or more generally, Many-Sided Stable Matching Problems). A natural question was posed: What system of preferences guarantees stable matching in many-sided problems? We give a partial answer to this question, using Latin rectangles.
Keywords: Many-sided matching, stable matching, latin rectangle, deferred acceptance algorithm
Received: 3 August 2025 Accepted: 12 September 2026
Published online: 12 September 2026