Abstract
Recently, we have introduced the notion of stable permutations in Latin squares. In this paper, we introduce the systems of I-M preferences in the marriage theory and we prove that in such a system, the study of stable marriages in two matrices is equivalent to the study of stable permutations in one matrix.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Dénes and A.D. Keedwell, Latin Squares and Their Applications. Academic Press. New York and London 1974.
D. Gale and L.S. Shapley, College admissions and the stability of marriages. Amer. Math. Monthly 69 (1962), 9–15.
J.S. Hwang, Stable permutations in Latin squares. Soochow J. Math. 4 (1978), 63–72.
J. S. Hwang, On the invariance of stable permutations in Latin rectangles (to appear in ARS Combinatoria).
D. E. Knuth, Mariages stables et leurs relations avec d'autres problèmes combinatoires. Les Presses de l'Université de Montréal 1976.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Hwang, J.S. (1981). Complete stable marriages and systems of I-M preferences. In: McAvaney, K.L. (eds) Combinatorial Mathematics VIII. Lecture Notes in Mathematics, vol 884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091807
Download citation
DOI: https://doi.org/10.1007/BFb0091807
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10883-2
Online ISBN: 978-3-540-38792-3
eBook Packages: Springer Book Archive