Journal of Integer Sequences, Vol. 22 (2019), Article 19.4.5

Enumeration of Border-Strip Decompositions and Weil-Petersson Volumes

Per Alexandersson
Department of Mathematics
Royal Institute of Technology
SE-100 44 Stockholm

Linus Jordan
Department of Mathematics
1015 Lausanne


We describe an injection from border-strip decompositions of certain diagrams to permutations. This allows us to provide enumeration results as well as q-analogues of enumeration formulas. Finally, we use this injection to prove a connection between the number of border-strip decompositions of the n × 2n rectangle and the Weil-Petersson volume of the moduli space of an n-punctured Riemann sphere.

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(Concerned with sequences A066319 A115047 A227404.)

Received May 28 2018; revised version received June 10 2019. Published in Journal of Integer Sequences, June 28 2019.

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