Catalan words are particular growth-restricted words over the set of non-negative integers, and they represent still another combinatorial class counted by the Catalan numbers. We study the distribution of descents on the sets of Catalan words avoiding a pattern of length at most three: for each such a pattern p we provide a bivariate generating function where the coefficient of xy in its serie...

Catalan numbers appear in many places throughout mathematics, and are a fairly frequent subject for articles in this magazine. Indeed, a very nice introduction to their properties was given in this magazine by Vun and Belcher [3], and a historical account of their discovery in Chinese mathematics (before Catalan!) has also appeared in a recent article by Larcombe [1]. The article by Vun and Bel...

This work studies Named Entity Classification (NEC) for Catalan without making use of large annotated resources of this language. Two views are explored and compared, namely exploiting solely the Catalan resources, and a direct training of bilingual classification models (Spanish and Catalan), given that a large collection of annotated examples is available for Spanish. The empirical results ob...

We summarize some combinatoric problems solved by the higher Catalan numbers. These problems are generalizations of the combinatoric problems solved by the Catalan numbers. The generating function of the higher Catalan numbers appeared recently as an auxiliary function in enumerating maps and explicit computations of the asymptotic expansion of the partition function of random matrices in the u...

This work studies Named Entity Recognition (NER) for Catalan without making use of annotated resources of this language. The approach presented is based on machine learning techniques and exploits Spanish resources, either by first training models for Spanish and then translating them into Catalan, or by directly training bilingual models. The resulting models are retrained on unlabelled Catala...

We present a large Spanish-Catalan parallel corpus extracted from ten years of the paper edition of a bilingual Catalan newspaper. The produced corpus of 7.5 M parallel sentences (around 180 M words per language) is useful for many natural language applications. We report excellent results when building a statistical machine translation system trained on this parallel corpus. The Spanish-Catala...

In the paper, the authors discover several series identities involving the Catalan numbers, the Catalan function, the Riemanian zeta function, and the alternative Hurwitz zeta function.

Let Cn and Cn(q) be the nth Catalan number and the nth q-Catalan number, respectively. In this paper, we show that the Diophantine equation Cn = Cm(q) has only finitely many integer solutions (m,n, q) with m > 1, n > 1, q > 1. Moreover, they are all effectively computable. – To Professor Carl Pomerance on his 65th birthday