Mathematics of Plott choice functions
组合数学
2007-05-23 v1
摘要
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
引用
@article{arxiv.math/0304171,
title = {Mathematics of Plott choice functions},
author = {V. I. Danilov and G. A. Koshevoy},
journal= {arXiv preprint arXiv:math/0304171},
year = {2007}
}
备注
25 pages, 6 figures