This paper describes the methodology followed to build a neural machine translation system in the biomedical domain for the English-Catalan language pair. This task can be considered a low-resourced task from the point of view of the domain and the language pair. To face this task, this paper reports experiments on a cascade pivot strategy through Spanish for the neural machine translation usin...

A Catalan triangulation of the MM obius band is an abstract simplicial complex triangulating the MM obius band which uses no interior vertices, and has vertices labelled 1; 2; : : : ; n in order as one traverses the boundary. We prove two results about the structure of this set, analogous to well-known results for Catalan triangulations of the disk. The rst is a generating function for Catalan ...

We describe arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects specified as a Haskell type class. Our algorithms work on a generic representation that we illustrate on instances members of the Catalan family, like ordered binary and multiway trees. We validate the correctness of our algorithms by defining an instance of the same type ...

We study novel arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects. Our algorithms work on a generic representation that we illustrate on instances like ordered binary and multiway trees, balanced parentheses languages as well as the usual bitstring-based natural numbers seen through the same generic interface as members of the Catalan...

We present new functional equations for the species of plane and of planar (in the sense of Harary and Palmer, 1973) 2-trees and some associated pointed species. We then deduce the explicit molecular expansion of these species, i.e. a classification of their structures according to their stabilizers. There result explicit formulas in terms of Catalan numbers for their associated generating seri...

In a recent article [11], Dukes, Flanagan, Mansour and Vajnovszki present Gray codes for several families of pattern avoiding permutations. In their Gray codes two consecutive objects differ in at most four or five positions, which is not optimal. In this paper, we present a unified construction in order to refine their results (or to find other Gray codes). In particular, we obtain more restri...

The notion of succession rule (system for short) provides a powerful tool for the enumeration of many classes of combinatorial objects. Often, different systems exist for a given class of combinatorial objects, and a number of problems arise naturally. An important one is the equivalence problem between two different systems. In this paper, we show how to solve this problem in the case of syste...

In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.

It may come as a surprise to many people to know that Spain in general and Catalonia in particular are probably the places in the world where machine translation systems are most extensively used for productive applications. The peculiar position of Catalan and Spanish in Catalonia, both being official and therefore mandatory for Public Administration publications and websites, the fact that Ca...

The q, t-Catalan numbers can be defined using rational functions, geometry related to Hilbert schemes, symmetric functions, representation theory, Dyck paths, partition statistics, or Dyck words. After decades of intensive study, it was eventually proved that all these definitions are equivalent. In this paper, we study the similar situation for higher q, t-Catalan numbers, where the equivalenc...