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Mathematics of Plott choice functions

V. I. Danilov·G. A. Koshevoy
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Abstract

This paper is devoted to a study of mathematical structures arising from choice functions satisfying the path independence property (Plott functions). We broaden the notion of a choice function by allowing of empty choice. This enables us to define a lattice structure on the set of Plott functions. Moreover, this lattice is functorially dependent on its base. We introduce a natural convex structure on the set of linear orders (or words) and show that Plott functions are in one-to-one correspondence with convex subsets in this set of linear orders. That correspondence is compatible with both lattice structures. Keywords: Convex geometries, shuffle, linear orders, lattices, direct image, path independence, convex structure

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V. I. Danilov, G. A. Koshevoy. 2003-04-14. Mathematics of Plott choice functions. https://arxiv.org/abs/math/0304171

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