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Abstract: |
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The property of ``substitutability'' plays a key role in guaranteeing |
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| the existence of a stable solution in the stable marriage problem and its |
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generalizations. On the other hand, the concept of M |
-convexity, introduced by |
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| Murota-Shioura (1999) for functions defined over the integer lattice, enjoys a number |
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| of nice properties that are expected of ``discrete convexity'' and provides with a |
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natural model of utility functions. In this note, we show that M |
-convexity is |
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| characterized by two variants of substitutability. |
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