A combinatorial representation of Arrow's single-peaked domains

2024/12/06 by Arkadii Slinko, Slinko, Arkadii
Computer Science · #91B14 #Advanced Algebra and Logic #Combinatorics (math.CO) #Constraint Satisfaction and Optimization #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2412.05406

openalex publication_date 2024/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The most studied class of Condorcet domains (acyclic sets of linear orders) is the class of peak-pit domains of maximal width. It has a number of combinatorial representations by such familiar combinatorial objects like rhombus tilings and arrangements of pseudolines. Arrow's single-peaked domains are peak-pit but do not have maximal width. We suggest how to represent them by means of generalised arrangements of pseudolines.

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