Enumeration of border-strip decompositions & Weil-Petersson volumes
Per Alexandersson, Linus Jordan

TL;DR
This paper introduces a permutation-based injection to enumerate border-strip decompositions, providing new formulas and linking these decompositions to Weil-Petersson volumes of moduli spaces.
Contribution
It presents a novel injection from border-strip decompositions to permutations, enabling enumeration and establishing a connection to Weil-Petersson volumes.
Findings
Enumeration formulas for border-strip decompositions
q-analogues of enumeration results
Link between border-strip counts and Weil-Petersson volumes
Abstract
We describe an injection from border-strip decompositions of certain shapes to permutations. This allows us to provide enumeration results, as well as -analogues of enumeration formulas. Finally, we use this injection to prove a connection between the number of border-strip decompositions of the rectangle and the Weil-Petersson volume of the moduli space of an -punctured Riemann sphere.
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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric and Algebraic Topology · Advanced Algebra and Geometry
