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A combinatorial representation of Arrow's single-peaked domains

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arxiv 2412.05406 v1 pith:BVMQ2J2T submitted 2024-12-06 math.CO

A combinatorial representation of Arrow's single-peaked domains

classification math.CO
keywords domainscombinatorialarrangementsarrowclassmaximalpeak-pitpseudolines
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. An axiomatic framework from splitting and merging in MAT-labeled graphs, vines, and single-peaked domains

    math.CO 2026-05 unverdicted novelty 7.0

    An axiomatic characterization using splitting and merging in combinatorial species shows that MAT-labeled complete graphs, regular vines, and maximal Arrow single-peaked domains share the same recursive structure, wit...

  2. An axiomatic framework from splitting and merging in MAT-labeled graphs, vines, and single-peaked domains

    math.CO 2026-05 unverdicted novelty 7.0

    Splitting and merging operations with compatibility conditions axiomatize and unify MAT-labeled complete graphs, regular vines, and maximal Arrow single-peaked domains, with further links to extremal lattices and tria...