Core Concepts
Height of random Tamari intervals scales as n^3/4 with an explicit limit law.
Abstract
The content discusses the scaling of random Tamari intervals and Schnyder woods in random triangulations. It delves into the exact solutions of models based on polynomial equations and D-finite tricks. The article explores the convergence of moments and the universality of the scaling phenomenon. Key insights include the bijection between intervals and triangulations, the role of the Tamari lattice in algebraic combinatorics, and the application of the D-finite method for moment pumping.
Stats
The height of a uniformly chosen vertex scales as n^3/4.
The number of elements in Tamari intervals is given by a specific formula.
The exact solution is based on polynomial equations with catalytic variables.
Quotes
"We show that the height of a uniformly chosen vertex scales as n^3/4."