2003/04/14 by V. I. Danilov, В. И. Данилов, Danilov, V. I. +3 · 1 citation
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Functional Equations Stability Results #Graph Labeling and Dimension Problems #Graph theory and applications #math.CO
paper · pdf · doi:10.48550/arxiv.math/0304171
25 pages, 6 figures
arxiv created 2003/04/14 · openalex publication_date 2003/04/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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