The uncrossing partial order on matchings is Eulerian
Thomas Lam
TL;DR
This paper proves that the partial order formed by resolving crossings in matchings of 2n points on a circle is an Eulerian poset, revealing a new combinatorial structure.
Contribution
It establishes that the crossing resolution poset on matchings is Eulerian, a novel insight into its combinatorial properties.
Findings
The crossing resolution poset is Eulerian.
The poset structure applies to matchings on a circle.
This reveals new symmetry in combinatorial matchings.
Abstract
We prove that the partial order on the set of matchings of 2n points on a circle, given by resolving crossings, is an Eulerian poset.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Algebra and Geometry