We exploit the 1983 language-in-education reform that introduced Catalan alongside Spanish as medium of instruction in Catalan schools to estimate the labour market value of bilingual education. Identification is achieved in a difference-in-differences framework exploiting variation in exposure to the reform across years of schooling and years of birth. We find positive wage returns to bilingua...

We introduce and study the number of tilings of unit height rectangles with irrational tiles. We prove that the class of sequences of these numbers coincides with the class of diagonals of N-rational generating functions and a class of certain binomial multisums. We then give asymptotic applications and establish connections to hypergeometric functions and Catalan numbers.

A leaf of a plane tree is called an old leaf if it is the leftmost child of its parent, and it is called a young leaf otherwise. In this paper we enumerate plane trees with a given number of old leaves and young leaves. The formula is obtained combinatorially by presenting two bijections between plane trees and 2-Motzkin paths which map young leaves to red horizontal steps, and old leaves to up...

This paper introduces a method for finding closed forms for certain sums involving squares of binomial coefficients. We use this method to present an alternative approach to a problem of evaluating a different type of sums containing squares of the numbers from Catalan's triangle.