Publication

Enumeration of Border-Strip Decompositions and Weil-Petersson Volumes

2019
Journal Articles

Abstract

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 x 2n rectangle and the Weil-Petersson volume of the moduli space of an n-punctured Riemann sphere.

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2019
Journal Articles

Abstract

Official source

Related concepts (17)

Moduli space

In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space.

Enumerative combinatorics

Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations. More generally, given an infinite collection of finite sets Si indexed by the natural numbers, enumerative combinatorics seeks to describe a counting function which counts the number of objects in Sn for each n.

Moduli of algebraic curves

In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves. It is thus a special case of a moduli space. Depending on the restrictions applied to the classes of algebraic curves considered, the corresponding moduli problem and the moduli space is different. One also distinguishes between fine and coarse moduli spaces for the same moduli problem.

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Enumeration of Border-Strip Decompositions and Weil-Petersson Volumes

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