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arXiv · 2412.05406

A combinatorial representation of Arrow's single-peaked domains

Arkadii Slinko
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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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Arkadii Slinko. 2024-12-06. A combinatorial representation of Arrow's single-peaked domains. https://arxiv.org/abs/2412.05406

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