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This study considers a school choice problem with general feasibility constraints. Each student belongs to a grade; and 2 students belonging to the same grade are symmetric, whereas those belonging to different grades can be asymmetric with respect to the feasibility constraint of a school. We introduce five requirements of a matching and a polynomial‐time algorithm to derive a matching satisfying them. Because the algorithm is inspired by the nursery school system of Yokohama City, we introduce the system and compare it with the algorithm of this study.

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